Some aspects of deformations of supersymmetric field theories

Journal of High Energy Physics

Volumn 4, Issue 5 PART A, 2000, Pages

  Ferrara, Sergio ^a   Lledó, María A ^b,c  

^a CERN   (Switzerland)

^b POLITECNICO DI TORINO   (Italy)

^c SEZIONE DI TORINO   (Italy)

Author keywords

Brane Dynamics in Gauge Theories; Extended Supersymmetry; Superspaces

Indexed keywords

EID: 7644244456     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/05/008     Document Type: Article

References (68)

1. H. Weyl, The theory of groups and quantum mechanics, Dover, New York 1931.
2. J. E. Moyal, Quantum mechanics as a statistical theory, Proc. Camb. Phil. Soc. 45 (1949) 99.
3. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, 1. Deformations of symplectic structures, Ann. Phys. (NY) 111 (1978) 61; Ann. Phys. (NY) 111 (1978) 111.
4. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, 1. Deformations of symplectic structures, Ann. Phys. (NY) 111 (1978) 61; Ann. Phys. (NY) 111 (1978) 111.
5. M. Kontsevich, Deformation quantization of Poisson manifolds, 1, math.QA/9709040.
6. A. Connes, M.R. Douglas and A. Schwarz, Noncommutative geometry and matrix theory: compactification on tori, J. High Energy Phys. 02 (1998) 003 [hep-th/9711162].
7. T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M-theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043].
8. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115].
9. A. Schwarz, Morita equivalence and duality, Nucl. Phys. B 534 (1998) 720 [hep-th/9805034]; D. Brace, B. Morariu and B. Zumino, Dualities of the matrix model from T-duality of the type-II string, Nucl. Phys. B 545 (1999) 192 [hep-th/9810099]; D. Brace, B. Morariu and B. Zumino, T-duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B 549 (1999) 181 [hep-th/9811213]; B. Pioline and A. Schwarz, Morita equivalence and T-duality (or B versus θ), J. High Energy Phys. 08 (1999) 021 [hep-th/9908019]; F. Lizzi, Strings, noncommutative geometry and the size of the target apace, Int. J. Mod. Phys. A 14 (1999) 4501 [hep-th/9902187].
10. A. Schwarz, Morita equivalence and duality, Nucl. Phys. B 534 (1998) 720 [hep-th/9805034]; D. Brace, B. Morariu and B. Zumino, Dualities of the matrix model from T-duality of the type-II string, Nucl. Phys. B 545 (1999) 192 [hep-th/9810099]; D. Brace, B. Morariu and B. Zumino, T-duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B 549 (1999) 181 [hep-th/9811213]; B. Pioline and A. Schwarz, Morita equivalence and T-duality (or B versus θ), J. High Energy Phys. 08 (1999) 021 [hep-th/9908019]; F. Lizzi, Strings, noncommutative geometry and the size of the target apace, Int. J. Mod. Phys. A 14 (1999) 4501 [hep-th/9902187].
11. A. Schwarz, Morita equivalence and duality, Nucl. Phys. B 534 (1998) 720 [hep-th/9805034]; D. Brace, B. Morariu and B. Zumino, Dualities of the matrix model from T-duality of the type-II string, Nucl. Phys. B 545 (1999) 192 [hep-th/9810099]; D. Brace, B. Morariu and B. Zumino, T-duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B 549 (1999) 181 [hep-th/9811213]; B. Pioline and A. Schwarz, Morita equivalence and T-duality (or B versus θ), J. High Energy Phys. 08 (1999) 021 [hep-th/9908019]; F. Lizzi, Strings, noncommutative geometry and the size of the target apace, Int. J. Mod. Phys. A 14 (1999) 4501 [hep-th/9902187].
12. A. Schwarz, Morita equivalence and duality, Nucl. Phys. B 534 (1998) 720 [hep-th/9805034]; D. Brace, B. Morariu and B. Zumino, Dualities of the matrix model from T-duality of the type-II string, Nucl. Phys. B 545 (1999) 192 [hep-th/9810099]; D. Brace, B. Morariu and B. Zumino, T-duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B 549 (1999) 181 [hep-th/9811213]; B. Pioline and A. Schwarz, Morita equivalence and T-duality (or B versus θ), J. High Energy Phys. 08 (1999) 021 [hep-th/9908019]; F. Lizzi, Strings, noncommutative geometry and the size of the target apace, Int. J. Mod. Phys. A 14 (1999) 4501 [hep-th/9902187].
13. A. Schwarz, Morita equivalence and duality, Nucl. Phys. B 534 (1998) 720 [hep-th/9805034]; D. Brace, B. Morariu and B. Zumino, Dualities of the matrix model from T-duality of the type-II string, Nucl. Phys. B 545 (1999) 192 [hep-th/9810099]; D. Brace, B. Morariu and B. Zumino, T-duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B 549 (1999) 181 [hep-th/9811213]; B. Pioline and A. Schwarz, Morita equivalence and T-duality (or B versus θ), J. High Energy Phys. 08 (1999) 021 [hep-th/9908019]; F. Lizzi, Strings, noncommutative geometry and the size of the target apace, Int. J. Mod. Phys. A 14 (1999) 4501 [hep-th/9902187].
14. B. Morariu and B. Zumino, Super Yang-Mills on the noncommutative torus, hep-th/9807198.
15. D. Brace and B. Morariu, A note on the BPS spectrum of the matrix model, J. High Energy Phys. 02 (1999) 004 [hep-th/9810185]; A. Konechny and A. Schwarz, BPS states on noncommutative tori and duality, Nucl. Phys. B 550 (1999) 561 [hep-th/9811159]; A. Konechny and A. Schwarz, 1/4-BP5 states on noncommutative tori, J. High Energy Phys. 09 (1999) 030 [hep-th/9907008].
16. D. Brace and B. Morariu, A note on the BPS spectrum of the matrix model, J. High Energy Phys. 02 (1999) 004 [hep-th/9810185]; A. Konechny and A. Schwarz, BPS states on noncommutative tori and duality, Nucl. Phys. B 550 (1999) 561 [hep-th/9811159]; A. Konechny and A. Schwarz, 1/4-BP5 states on noncommutative tori, J. High Energy Phys. 09 (1999) 030 [hep-th/9907008].
17. D. Brace and B. Morariu, A note on the BPS spectrum of the matrix model, J. High Energy Phys. 02 (1999) 004 [hep-th/9810185]; A. Konechny and A. Schwarz, BPS states on noncommutative tori and duality, Nucl. Phys. B 550 (1999) 561 [hep-th/9811159]; A. Konechny and A. Schwarz, 1/4-BP5 states on noncommutative tori, J. High Energy Phys. 09 (1999) 030 [hep-th/9907008].
18. C. Hofman and E. Verlinde, U-duality of Born-Infeld on the noncommutative twotorus, J. High Energy Phys. 12 (1998) 010 [hep-th/9810116]; C. Hofman and E. Verlinde, Gauge bundles and Born-Infeld on the noncommutative torus, Nucl. Phys. B 547 (1999) 157 [hep-th/9810219].
19. C. Hofman and E. Verlinde, U-duality of Born-Infeld on the noncommutative twotorus, J. High Energy Phys. 12 (1998) 010 [hep-th/9810116]; C. Hofman and E. Verlinde, Gauge bundles and Born-Infeld on the noncommutative torus, Nucl. Phys. B 547 (1999) 157 [hep-th/9810219].
20. R. D'Auria, S. Ferrara and M.A. Lledó, On central charges and hamiltonians for 0-brane dynamics, Phys. Rev. D 60 (1999) 084007 [hep-th/9903089].
21. M.R. Douglas and C. Hull, D-branes and the noncommutative torus, J. High Energy Phys. 02 (1998) 008 [hep-th/9711165].
22. A. Connes, Noncommutative geometry, Academic Press, 1994.
23. N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys. 09 (1999) 032 [hep-th/9908142].
24. J. Madore, S. Schraml, P. Schupp and J. Wess, Gauge theory on noncommutative spaces, hep-th/0001203.
25. S. Minwalla, M.V. Raamsdonk and N. Seiberg, Noncommutative perturbative dynamics, hep-th/9912072.
26. S. Cecotti and S. Ferrara, Supersymmetric Born-Infeld lagrangians, Phys. Lett. B 187 (1997) 335.
27. J. Bagger and A. Galperin, A new goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177].
28. A. Schwarz, Noncommutative supergeometry and duality, hep-th/9912212.
29. C.-S. Chu and F. Zamora, Manifest supersymmetry in non-commutative geometry, J. High Energy Phys. 02 (2000) 022 [hep-th/9912153].
30. D. Minic, M-theory and deformation quantization, hep-th/9909022.
31. A. Jevicki and S. Ramgoolam, Non-commutative gravity from the AdS/CFT correspondence, J. High Energy Phys. 04 (1999) 032 [hep-th/9902059]; Z. Chang, Quantum anti-de Sitter space, hep-th/9904091; H. Steinacker, Quantum anti-de Sitter space and sphere at roots of unity, hep-th/9910037.
32. A. Jevicki and S. Ramgoolam, Non-commutative gravity from the AdS/CFT correspondence, J. High Energy Phys. 04 (1999) 032 [hep-th/9902059]; Z. Chang, Quantum anti-de Sitter space, hep-th/9904091; H. Steinacker, Quantum anti-de Sitter space and sphere at roots of unity, hep-th/9910037.
33. A. Jevicki and S. Ramgoolam, Non-commutative gravity from the AdS/CFT correspondence, J. High Energy Phys. 04 (1999) 032 [hep-th/9902059]; Z. Chang, Quantum anti-de Sitter space, hep-th/9904091; H. Steinacker, Quantum anti-de Sitter space and sphere at roots of unity, hep-th/9910037.
34. R.J. Finkelstein, Q-gravity, Lett. Math. Phys. 38 (1996) 53.
35. L. Castellani, Gauge theories of quantum groups, Phys. Lett. B 292 (1992) 93 [hep-th/9205103].
36. F.A. Berezin and M.S. Marinov, Particle spin dynamics as the Grassmann variant of classical mechanics, Ann. Phys. (NY) 104 (1977) 336.
37. I. A. Batalin and E. S. Fradkin, Operator quantization and abelization of dynamical systems subject to first-class constraints, Riv. Nuov. Cim. 9 n.10 (1986) 6; Operatorial quantization of dynamical systems subject to constraints. A further study of the construction, Ann. Inst. Henri Poincaré. 49, n. 2 (1988) 145; M.A. Vasiliev, Extended higher spin superalgebras and their realizations in terms of quantum operators, Fortschr. Phys. 36 (1988) 33.
38. I. A. Batalin and E. S. Fradkin, Operator quantization and abelization of dynamical systems subject to first-class constraints, Riv. Nuov. Cim. 9 n.10 (1986) 6; Operatorial quantization of dynamical systems subject to constraints. A further study of the construction, Ann. Inst. Henri Poincaré. 49, n. 2 (1988) 145; M.A. Vasiliev, Extended higher spin superalgebras and their realizations in terms of quantum operators, Fortschr. Phys. 36 (1988) 33.
39. I. A. Batalin and E. S. Fradkin, Operator quantization and abelization of dynamical systems subject to first-class constraints, Riv. Nuov. Cim. 9 n.10 (1986) 6; Operatorial quantization of dynamical systems subject to constraints. A further study of the construction, Ann. Inst. Henri Poincaré. 49, n. 2 (1988) 145; M.A. Vasiliev, Extended higher spin superalgebras and their realizations in terms of quantum operators, Fortschr. Phys. 36 (1988) 33.
40. D.B. Fairlie and C.K. Zachos, Infinite dimensional algebras, sine brackets and SU(∞), Phys. Lett. B 224 (1989) 101.
41. E. S. Fradkin and V. Ya. Linetsky, Quantization and cocycles on the supertorus and large-N limits for the classical Lie superalgebras, Mod. Phys. Lett. A 6 (1991) 217.
42. R. Abraham and J. E. Marsden, Foundations of mechanics Addison-Wesley Publishing Company, 1978.
43. J.L. Martin, Generalized classical dynamics and the 'classical analogue' of a Fermi oscilator, Proc. Roy. Soc. A251 (1959) 536.
44. A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 matter, Yang-Mills and supergravity theories in harmonic superspace, Class. and Quant. Grav. 1 (1984) 469; E. Ivanov, S. Kalitzin, N. Ai Viet and V. Ogievetsky, Harmonic superspaces of extended supersymmetry, the calculus of harmonic variables, J. Phys. 18 (1985) 3433.
45. A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 matter, Yang-Mills and supergravity theories in harmonic superspace, Class. and Quant. Grav. 1 (1984) 469; E. Ivanov, S. Kalitzin, N. Ai Viet and V. Ogievetsky, Harmonic superspaces of extended supersymmetry, the calculus of harmonic variables, J. Phys. 18 (1985) 3433.
46. S. Ferrara and E. Sokatchev, Short representations of SU(2, 2/N) and harmonic superspace analyticity, hep-th/9912168.
47. I.Y. Aref'eva, D.M. Belov and A.S. Koshelev, A note on UV/IR for noncommutative complex scalar field, hep-th/0001215.
48. J. Wess and B. Zumino, Supergauge transformations in four-dimensions, Nucl. Phys. B 70 (1974) 39; A lagrangian model invariant under supergauge transformations, Phys. Lett. B 49 (1974) 52.
49. J. Wess and B. Zumino, Supergauge transformations in four-dimensions, Nucl. Phys. B 70 (1974) 39; A lagrangian model invariant under supergauge transformations, Phys. Lett. B 49 (1974) 52.
50. J. Iliopoulos and B. Zumino, Broken supergauge symmetry and renormalization, Nucl. Phys. B 76 (1974) 310.
51. S. Ferrara, J. Iliopoulos and B. Zumino, Supergauge invariance and the Gell-Mannlow eigenvalue, Nucl. Phys. B 77 (1974) 413.
52. S. Ferrara, J. Wess and B. Zumino, Supergauge multiplets and superfields, Phys. Lett. B 51 (1974) 239.
53. J. Wess and B. Zumino, Supergauge invariant extension of quantum electrodynamics, Nucl. Phys. B 78 (1974) 1.
54. S. Ferrara and B. Zumino, Supergauge invariant Yang-Mills theories, Nucl. Phys. B 79 (1974) 413.
55. d, 1. Scalars, hep-th/9911098.
56. W. Fischler et al., Evidence for winding states in noncommutative quantum field theory, J. High Energy Phys. 05 (2000) 024 [hep-th/0002067].
57. A. Matusis, L. Susskind and N. Toumbas, The IR/UV connection in the non-commutative gauge theories, hep-th/0002075.
58. R. Kallosh, N = 3 harmonic superspace, Pis'ma ZHETF 41 (1985) 172, Sov. Phys. JETP Lett. 41 (1985) 209.
59. R. Kallosh, N = 3 harmonic superspace, Pis'ma ZHETF 41 (1985) 172, Sov. Phys. JETP Lett. 41 (1985) 209.
60. P.S. Howe and P.C. West, Operator product expansions in four-dimensional superconformal field theories, Phys. Lett. B 389 (1996) 273 [hep-th/9607060]; Superconformal invariants and extended super symmetry, Phys. Lett. B 400 (1997) 307 [hep-th/9611075].
61. P.S. Howe and P.C. West, Operator product expansions in four-dimensional superconformal field theories, Phys. Lett. B 389 (1996) 273 [hep-th/9607060]; Superconformal invariants and extended super symmetry, Phys. Lett. B 400 (1997) 307 [hep-th/9611075].
62. 5 and N = 4, D = 4 primary superfields, Phys. Rev. D 58 (1998) 105029 [hep-th/9805082].
63. S.V. Ketov, A manifestly N = 2 supersymmetric Born-Infeld action, Mod. Phys. Lett. A 14 (1999) 501 [hep-th/9809121].
64. A.A. Tseytlin, Born-Infeld action, supersymmetry and string theory, hep-th/9908105; M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and 3-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232].
65. A.A. Tseytlin, Born-Infeld action, supersymmetry and string theory, hep-th/9908105; M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and 3-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232].
66. S.M. Kuzenko and S. Theisen, Supersymmetric duality rotations, J. High Energy Phys. 03 (2000) 034 [hep-th/0001068].
67. P.S. Howe, K.S. Stelle and P.K. Townsend, Superactions, Nucl. Phys. B 191 (1981) 445; Supercurrents, Nucl. Phys. B 192 (1981) 332.
68. P.S. Howe, K.S. Stelle and P.K. Townsend, Superactions, Nucl. Phys. B 191 (1981) 445; Supercurrents, Nucl. Phys. B 192 (1981) 332.