Integrable systems and supersymmetric gauge theory

Nuclear Physics B

Volumn 459, Issue 1-2, 1996, Pages 97-112

  Martinec, Emil J ^a   Warner, Nicholas P ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030583978     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/0550-3213(95)00588-9     Document Type: Article

References (50)

1. [1] N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19; B 430 (1994) 485 (E).
2. [1] N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19; B 430 (1994) 485 (E).
3. [2] A. Klemm, W. Lerche, S. Yankielowicz and S. Theisen, Simple singularities and N = 2 supersymmetric Yang-Mills theory, Phys. Lett. B 344 (1995) 169.
4. [3] P.C. Argyres and A. Faraggi, The vacuum structure and spectrum of N = 2 supersymmetric SU(N) gauge theory, Phys. Rev. Lett. 74 (1995) 3931.
5. [4] U.H. Danielsson and B. Sundborg, The moduli space and monodromies of N = 2 supersymmetric SO(2R + 1) Yang-Mills theory, hep-th/9504102.
6. [5] A. Brandhuber and K. Landsteiner, On the monodromies of N = 2 supersymmetric Yang-Mills theory with gauge group SO(2N), hep-th/9507008.
7. [6] A. Gorskii, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, Integrability and Seiberg-Witten exact solution, Phys. Lett. B 355 (1995) 466.
8. [7] I.M. Krichever, Methods of algebraic geometry in the theory of nonlinear equations, Russ. Math. Surveys 32 (1977) 185; P. van Moerbeke and D. Mumford, The spectrum of difference operators and algebraic curves, Acta Math. 143 (1979) 93.
9. [7] I.M. Krichever, Methods of algebraic geometry in the theory of nonlinear equations, Russ. Math. Surveys 32 (1977) 185; P. van Moerbeke and D. Mumford, The spectrum of difference operators and algebraic curves, Acta Math. 143 (1979) 93.
10. [8] V. Kac, Infinite dimensional Lie algebras (Cambridge Press, Cambridge, 1983).
11. [9] O. Bogoyavlenski, On perturbations of the periodic Toda lattices, Comm. Math. Phys. 51 (1976) 201.
12. [10] M. Adler and P. van Moerbeke, Kowalewski's asymptotic method, Kac-Moody Lie algebras, and regularization, Comm. Math. Phys. 83 (1982) 83.
13. [11] See, for instance, D. Olive and N. Turok, Algebraic structure of Toda systems, Nucl. Phys. B 220 (1983) 491.
14. [12] M. Adler and P. van Moerbeke, Completely integrable systems, Euclidean Lie algebras, and curves, Adv. Math. 38 (1980) 267; Linearization of Hamiltonian systems, Jacobi varieties, and representation theory, Adv. Math. 38 (1980) 318.
15. [12] M. Adler and P. van Moerbeke, Completely integrable systems, Euclidean Lie algebras, and curves, Adv. Math. 38 (1980) 267; Linearization of Hamiltonian systems, Jacobi varieties, and representation theory, Adv. Math. 38 (1980) 318.
16. [13] A. McDaniel, Representations of SL(n,ℂ) and the Toda lattice, Duke Math. J. 56 (1988) 47.
17. [14] A. McDaniel and L. Smolinsky, A Lie theoretic Galois theory for the spectral curves of an integrable system: I, Comm. Math. Phys. 149 (1992) 127.
18. [15] V. Kanev, Spectral curves, simple Lie algebras, and Prym-Tjurin varieties, in: Theta Functions, Bowdoin 1987, Proc. Symp. Pure Math. 49, L. Ehrenpreis and R. Gunning, eds., AMS, Providence (1989).
19. [16] R. Donagi, Decomposition of spectral covers, in: Journées de Geometrie Algébrique d'Orsay, Asterisque Vol. 218, Soc. Math. de France, Paris (1993).
20. [17] H. Flaschka and D. McLaughlin, Canonically conjugate variables for the KdV equation and the Toda lattice with periodic boundary conditions. Prog. Theor. Phys. 55 (1976) 438.
21. [18] P. van Moerbeke, The spectrum of Jacobi matrices, Inv. Math. 37 (1976) 45.
22. [19] M.R. Adams, J. Harnad and J. Hurtubise, Darboux coordinates and Liouville-Arnold integration in loop algebras, Comm. Math. Phys. 155 (1993) 385.
23. [20] I.M. Krichever, Whitham theory for integrable systems and topological quantum field theories, in: New Symmetry Principles in Quantum Field Theory, J. Frohlich et al. eds., NATO ASI Series B, Vol. 295 (Plenum Press, NY, 1992).
24. [21] I.M. Krichever, The tau function of the universal Whitham hierarchy, matrix models and topological field theories, Comm. Pure Appl. Math. 47 (1994) 437.
25. [22] B. Dubrovin, Integrable systems in topological field theory, Nucl. Phys. B 379 (1992) 627.
26. [23] M.F. Atiyah and N.J. Hitchin, Low-energy scattering of nonabelian magnetic monopoles, Philos. Trans. R. Soc. Lond. 315 (1985) 459.
27. [24] For reviews, see P. Di Francesco, P. Ginsparg and J. Zinn-Justin, 2-D gravity and random matrices, Phys. Rept. 254 (1995) 1; P. Ginsparg and G. Moore, Lectures on 2nd gravity and 2d string theory, Lectures given at TASI summer school, Boulder CO (June 11-19, 1992), published in Boulder TASI 92, pp. 277-470; R. Dijkgraaf, Intersection theory, integrable hierarchies and topological field theory, in: New Symmetry Principles in Quantum Field Theory, J. Frohlich et al. eds., NATO ASI Series B, Vol. 295 (Plenum Press, NY, 1992).
28. [24] For reviews, see P. Di Francesco, P. Ginsparg and J. Zinn-Justin, 2-D gravity and random matrices, Phys. Rept. 254 (1995) 1; P. Ginsparg and G. Moore, Lectures on 2nd gravity and 2d string theory, Lectures given at TASI summer school, Boulder CO (June 11-19, 1992), published in Boulder TASI 92, pp. 277-470; R. Dijkgraaf, Intersection theory, integrable hierarchies and topological field theory, in: New Symmetry Principles in Quantum Field Theory, J. Frohlich et al. eds., NATO ASI Series B, Vol. 295 (Plenum Press, NY, 1992).
29. [24] For reviews, see P. Di Francesco, P. Ginsparg and J. Zinn-Justin, 2-D gravity and random matrices, Phys. Rept. 254 (1995) 1; P. Ginsparg and G. Moore, Lectures on 2nd gravity and 2d string theory, Lectures given at TASI summer school, Boulder CO (June 11-19, 1992), published in Boulder TASI 92, pp. 277-470; R. Dijkgraaf, Intersection theory, integrable hierarchies and topological field theory, in: New Symmetry Principles in Quantum Field Theory, J. Frohlich et al. eds., NATO ASI Series B, Vol. 295 (Plenum Press, NY, 1992).
30. [25] M. Adler and P. van Moerbeke, The Toda lattice, Dynkin diagrams, singularities and Abelian varieties, Inv. Math. 103 (1991) 223; M. Adler, L. Haine and P. van Moerbeke, Limit matrices for the Toda flow and periodic flags for loop groups, Math. Ann. 296 (1993) 1.
31. [25] M. Adler and P. van Moerbeke, The Toda lattice, Dynkin diagrams, singularities and Abelian varieties, Inv. Math. 103 (1991) 223; M. Adler, L. Haine and P. van Moerbeke, Limit matrices for the Toda flow and periodic flags for loop groups, Math. Ann. 296 (1993) 1.
32. [26] P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93.
33. [27] N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484.
34. [28] A. Hanany and Y. Oz, On the quantum moduli space of vacua of N = 2 supersymmetric SU(N) gauge theories, hep-th/9505075.
35. [29] P.C. Argyres, M.R. Plesser and A.D. Shapere, The Coulomb phase of N = 2 supersymmetric QCD, Phys. Rev. Lett. 75 (1995) 1699.
36. [30] J.A. Minahan and D. Nemeschansky, Hyperelliptic curves for supersymmetric Yang-Mills, hep-th/9507032.
37. [31] S. Cecotti and C. Vafa, Topological antitopological fusion, Nucl. Phys. B 367 (1991) 359; Exact results for supersymmetric sigma models, Phys. Rev. Lett. 68 (1992) 903; On classification of N = 2 supersymmetric theories, Comm. Math. Phys. 158 (1993) 569.
38. [31] S. Cecotti and C. Vafa, Topological antitopological fusion, Nucl. Phys. B 367 (1991) 359; Exact results for supersymmetric sigma models, Phys. Rev. Lett. 68 (1992) 903; On classification of N = 2 supersymmetric theories, Comm. Math. Phys. 158 (1993) 569.
39. [31] S. Cecotti and C. Vafa, Topological antitopological fusion, Nucl. Phys. B 367 (1991) 359; Exact results for supersymmetric sigma models, Phys. Rev. Lett. 68 (1992) 903; On classification of N = 2 supersymmetric theories, Comm. Math. Phys. 158 (1993) 569.
40. [32] S. Ferrara, J.A. Harvey, A. Strominger and C. Vafa, Second quantized mirror symmetry, hep-th/9505162.
41. N WZW Models, Nucl. Phys. B 347 (1990) 687; S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417; E.J. Mlawer, S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality of WZW Fusion Coefficients and Chern-Simons Link Observables, Nucl. Phys. B 352 (1991) 863; D. Altschuler, M. Bauer and H. Saleur, Level Rank Duality in Nonunitary Coset Theories, J. Phys. A 23 (1990) L789; H. Saleur and D. Altschuler, Level Rank Duality in Quantum Groups, Nucl. Phys. B 354 (1991) 579; T. Nakanishi and A. Tsuchiya, Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992) 351.
42. N WZW Models, Nucl. Phys. B 347 (1990) 687; S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417; E.J. Mlawer, S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality of WZW Fusion Coefficients and Chern-Simons Link Observables, Nucl. Phys. B 352 (1991) 863; D. Altschuler, M. Bauer and H. Saleur, Level Rank Duality in Nonunitary Coset Theories, J. Phys. A 23 (1990) L789; H. Saleur and D. Altschuler, Level Rank Duality in Quantum Groups, Nucl. Phys. B 354 (1991) 579; T. Nakanishi and A. Tsuchiya, Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992) 351.
43. N WZW Models, Nucl. Phys. B 347 (1990) 687; S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417; E.J. Mlawer, S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality of WZW Fusion Coefficients and Chern-Simons Link Observables, Nucl. Phys. B 352 (1991) 863; D. Altschuler, M. Bauer and H. Saleur, Level Rank Duality in Nonunitary Coset Theories, J. Phys. A 23 (1990) L789; H. Saleur and D. Altschuler, Level Rank Duality in Quantum Groups, Nucl. Phys. B 354 (1991) 579; T. Nakanishi and A. Tsuchiya, Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992) 351.
44. N WZW Models, Nucl. Phys. B 347 (1990) 687; S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417; E.J. Mlawer, S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality of WZW Fusion Coefficients and Chern-Simons Link Observables, Nucl. Phys. B 352 (1991) 863; D. Altschuler, M. Bauer and H. Saleur, Level Rank Duality in Nonunitary Coset Theories, J. Phys. A 23 (1990) L789; H. Saleur and D. Altschuler, Level Rank Duality in Quantum Groups, Nucl. Phys. B 354 (1991) 579; T. Nakanishi and A. Tsuchiya, Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992) 351.
45. N WZW Models, Nucl. Phys. B 347 (1990) 687; S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417; E.J. Mlawer, S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality of WZW Fusion Coefficients and Chern-Simons Link Observables, Nucl. Phys. B 352 (1991) 863; D. Altschuler, M. Bauer and H. Saleur, Level Rank Duality in Nonunitary Coset Theories, J. Phys. A 23 (1990) L789; H. Saleur and D. Altschuler, Level Rank Duality in Quantum Groups, Nucl. Phys. B 354 (1991) 579; T. Nakanishi and A. Tsuchiya, Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992) 351.
46. N WZW Models, Nucl. Phys. B 347 (1990) 687; S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417; E.J. Mlawer, S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality of WZW Fusion Coefficients and Chern-Simons Link Observables, Nucl. Phys. B 352 (1991) 863; D. Altschuler, M. Bauer and H. Saleur, Level Rank Duality in Nonunitary Coset Theories, J. Phys. A 23 (1990) L789; H. Saleur and D. Altschuler, Level Rank Duality in Quantum Groups, Nucl. Phys. B 354 (1991) 579; T. Nakanishi and A. Tsuchiya, Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992) 351.
47. N WZW Models, Nucl. Phys. B 347 (1990) 687; S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417; E.J. Mlawer, S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality of WZW Fusion Coefficients and Chern-Simons Link Observables, Nucl. Phys. B 352 (1991) 863; D. Altschuler, M. Bauer and H. Saleur, Level Rank Duality in Nonunitary Coset Theories, J. Phys. A 23 (1990) L789; H. Saleur and D. Altschuler, Level Rank Duality in Quantum Groups, Nucl. Phys. B 354 (1991) 579; T. Nakanishi and A. Tsuchiya, Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992) 351.
48. [34] C. Vafa, Topological Landau-Ginzburg models, Mod. Phys. Lett. A 6 (1991) 337.
49. [35] S. Kachru, A. Klemm, W. Lerche, P. Mayr and Cumrun Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, to be published in Nucl. Phys. B 459, No. 3 (1996).
50. [36] R. Donagi and E. Markman, Cubics, integrable systems, and Calabi-Yau threefolds, to appear in the proceedings of the Algebraic Geometry Workshop on the occasion of the 65th birthday of F. Hirzebruch, May 1993; alg-geom/9408004.