Moyal deformation, Seiberg-Witten maps, and integrable models

Letters in Mathematical Physics

Volumn 54, Issue 2, 2000, Pages 123-135

  Dimakis, A ^a   Muller Hoissen F ^b  

^a UNIVERSITY OF THE AEGEAN   (Greece)

^b MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

Deformation quantization; Integrable model; Seiberg Witten map; Star product

Indexed keywords

EID: 0013140393     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011028111581     Document Type: Article

References (28)

1. Seiberg, N. and Witten, E.: String theory and noncommutative geometry, J. High Energy Phys. 9 (1999), 32.
2. Asakawa, T. and Kishimoto, I.: Comments on gauge equivalence in noncommutative geometry, J. High Energy Phys. 11 (1999), 24.
3. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
4. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
5. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
6. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
7. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
8. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
9. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
10. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys.; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
11. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
12. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
13. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
14. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
15. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
16. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
17. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
18. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in θ, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
19. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
20. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
21. Cornalba, L.: D-brane physics and noncommutative Yang-Mills theory, hep-th/9909081; Ishibashi, N.: A relation between commutative and noncommutative descriptions of D-branes, hep-th/9909176; Ishibashi, N., Iso, S., Kawai, H. and Kitazawa, Y.: Wilson loops in non-commutative Yang-Mills, Nuclear Phys. B 573 (2000), 573; Okuyama, K.: A path integral representation of the map between commutative and noncommutative gauge fields, J. High Energy Phys. 3 (2000), 16; Chu, C.-S., Ho, P.-M. and Li, M.: Matrix theory in a constant C field background, Nuclear Phys. B 574 (2000), 275; Andreev, O. and Dorn, H.: On open string sigma-model and noncommutative gauge fields, hep-th/9912070; Jurco, B. and Schupp, P.: Noncommutative Yang-Mills from equivalence of star products, hep-th/0001032; Terashima, S.: On the equivalence between noncommutative and ordinary gauge theories, hep-th/0001111, to appear in J. High Energy Phys,; Madore, J., Schraml, S., Schupp, P. and Wess, J.: Gauge theory on noncommutative spaces, hep-th/0001203; Hashimoto, K. and Hirayama, T.: Branes and BPS configurations of non-commutative/commutative gauge theories, hep-th/0002090; Asakawa, T. and Kishimoto, I.: Noncommutative gauge theories from deformation quantization, hep-th/0002138; Alekseev, A. Y. and Bytsko, A. G.: Wilson lines on noncommutative tori, Phys. Lett. B 482 (2000), 271; Moriyama, S.: Noncommutative monopole from nonlinear monopole, hep-th/0003231; Benaoum, H. B.: On noncommutative and commutative equivalence for BFYM theory: Seiberg-Witten map, hep-th/0004002; Jurco, B., Schupp, P. and Wess, J.: Noncommutative gauge theory for Poisson manifolds, hep-th/0005005; Goto, S. and Hata, H.: Noncommutative monopole at the second order in 0, hep-th/0005101; Terashima, S.: The non-Abelian Born-Infeld action and noncommutative gauge theory, hep-th/0006058; Jurco, B., Schraml, S., Schupp, P. and Wess, J.; Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces, hep-th/0006246; Rey, S.-J. and von Unge, R.: S-duality, noncritical open string and noncommutative gauge theory, hep-th/0007089.
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