Duality rotations in nonlinear electrodynamics and in extended supergravity

Rivista del Nuovo Cimento

Volumn 31, Issue 11, 2008, Pages 625-707

  Aschieri, P ^a,b   Ferrara, S ^c,d,e   Zumino, B ^f  

^a MUSEO STORICO DELLA FISICA E CENTRO STUDI E RICERCHE ENRICO FERMI   (Italy)

^b UNIVERSITY OF EASTERN PIEDMONT   (Italy)

^c CERN   (Switzerland)

^d INFN LABORATORI NAZIONALI DI FRASCATI   (Italy)

^e UNIVERSITY OF CALIFORNIA   (United States)

^f UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 61349198176     PISSN: 0393697X     EISSN: None     Source Type: Journal    
DOI: 10.1393/ncr/i2008-10038-8     Document Type: Review

References (111)

1. BORN M. and INFELD L., Foundations of the New Field Theory, Proc. R. Soc. London, Ser. A, 144 (1934) 425.
2. SCHRÖDINGER E., Contributions to Born's New Theory of the Electromagnetic Field, Proc. R. Soc. London, Ser. A, 150 (1935) 465.
3. FERRARA S., SCHERK J. and ZUMINO B., Algebraic Properties of Extended Supergravity Theories, Nucl. Phys. B, 121 (1977) 393.
4. CREMMER E., SCHERK J. and FERRARA S., SU(4) Invariant Supergravity Theory, Phys. Lett. B, 74 (1978) 61.
5. CREMMER E. and JULIA B., The SO(8) Supergravity, Nucl. Phys. B, 159 (1979) 141;
6. CREMMER E. and JULIA B., The N = 8 Supergravity Theory. 1. The Lagrangian, Phys. Lett. B, 80 (1978) 48.
7. GAILLARD M. K. and ZUMINO B., Duality Rotations for Interacting Fields, Nucl. Phys. B, 193 (1981) 221.
8. ZUMINO B., Quantum Structure of Space and Time, edited by DUFF M. J. and ISHAM C. J. (Cambridge University Press) 1982, p. 363.
9. CASTELLANI L., D'AURIA R. and FRÉ P., Supergravity and Superstrings: a Geometric Perspective (World Scientific) 1991.
10. CERESOLE A., D'AURIA R., FERRARA S. and VAN PROEYEN A., Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity, Nucl. Phys. B, 444 (1995) 92 [arXiv:hep-th/9502072].
11. ANDRIANOPOLI L., D'AURIA R., FERRARA S., FRÉ P. and TRIGIANTE M., R-R Scalars, U-Duality and Solvable Lie Algebras, Nucl. Phys. B, 496 (1997) 617 [arXiv:hep-th/9611014].
12. ANDRIANOPOLI L., D'AURIA R. and FERRARA S., U-duality and central charges in various dimensions revisited, Int. J. Mod. Phys. A, 13 (1998) 431 [arXiv:hep-th/9612105].
13. GIBBONS G. W. and RASHEED D. A., Electric-Magnetic Duality Rotations in Non-Linear Electrodynamics, Nucl. Phys. B, 454 (1995) 185; [arXiv:hep-th/9506035].
14. GIBBONS G. W. and RASHEED D. A., SL(2, R) Invariance of Nonlinear Electrodynamics Coupled to an Axion and Dilaton, Phys. Lett. B, 365 (1996) 46; [arXiv:hep-th/9509141].
15. GAILLARD M. K. and ZUMINO B., Self-Duality in Nonlinear Electromagnetism, in Supersymmetry and Quantum Field Theory, Kharkov 1997, edited by WESS J. and AKULOV V. P. (Springer-Verlag) 1998; [arXiv:hep-th/9705226].
16. GAILLARD M. K. and ZUMINO B., Nonlinear Electromagnetic Self-Duality and Legendre Transformations, in Duality and Supersymmetric Theories, edited by OLIVE D. I. and WEST P. C. (Cambridge University Press) 1999; [arXiv:hep-th/9712103].
17. ARAKI M. and TANII Y., Duality Symmetries in Nonlinear Gauge Theories, Int. J. Mod. Phys. A, 14 (1999) 1139; [arXiv:hep-th/9808029].
18. BRACE D., MORARIU B. and ZUMINO B., Duality Invariant Born-Infeld Theory, Yuri Golfand memorial volume; [arXiv:hep-th/9905218].
19. ASCHIERI P., BRACE D., MORARIU B. and ZUMINO B., Nonlinear self-duality in even dimensions, Nucl. Phys. B, 574 (2000) 551 [arXiv:hep-th/9909021].
20. ASCHIERI P., BRACE D., MORARIU B. and ZUMINO B., Proof of a symmetrized trace conjecture for the Abelian Born-Infeld Lagrangian, Nucl. Phys. B, 588 (2000) 521 [arXiv:hep-th/0003228].
21. IVANOV E. A. and ZUPNIK B. M., New representation for Lagrangians of self-dual nonlinear electrodynamics, talk given at the International Workshop on Supersymemtry and Quantum Symmetry (SQS '01): 16th Max Born Symposium, Karpacz, Poland, 21-25 Sep 2001, in Karpacz 2001, Supersymmetries and quantum symmetries, 235-250, [arXiv:hep-th/0202203];
22. IVANOV E. A. and ZUPNIK B. M., New approach to nonlinear electrodynamics: Dualities as symmetries of interaction, Phys. At. Nucl., 67 (2004) 2188
23. (Yad. Fiz., 67 (2004) 2212) [arXiv:hep-th/0303192].
24. ANTONIADIS I., PARTOUCHE H. and TAYLOR T. R., Spontaneous Breaking of N = 2 Global Supersymmetry, Phys. Lett. B, 372 (1996) 83; [arXiv:hep-th/9512006].
25. ROCEK M. and TSEYTLIN A. A., Partial breaking of global D = 4 supersymmetry, constrained superfields, and 3-brane actions, Phys. Rev. D, 59 (1999) 106001; [arXiv:hep-th/9811232].
26. KUZENKO S. M. and THEISEN S., Supersymmetric duality rotations, JHEP, 0003 (2000) 034 [arXiv:hep-th/0001068].
27. KUZENKO S. M. and THEISEN S., Nonlinear self-duality and supersymmetry, Fortsch. Phys., 49 (2001) 273 [arXiv:hep-th/0007231].
28. KUZENKO S. M. and MCCARTHY S. A., Nonlinear self-duality and supergravity, JHEP, 0302 (2003) 038 [arXiv:hep-th/0212039].
29. KUZENKO S. M. and MCCARTHY S. A., On the component structure of N = 1 supersymmetric nonlinear electrodynamics, JHEP, 0505 (2005) 012 [arXiv:hep-th/0501172].
30. TANII Y., N = 8 Supergravity in Six-Dimensions, Phys. Lett. B, 145 (1984) 197.
31. CECOTTI S., FERRARA S. and GIRARDELLO L., Hidden Noncompact Symmetries in String Theory, Nucl. Phys. B, 308 (1988) 436.
32. JULIA B. L., Dualities in the classical supergravity limits, in Strings Brunes and Dualities, Cargese (1997) p. 121; [arXiv:hep-th/9805083].
33. HULL C. M. and TOWNSEND P. K., Unity of superstring dualities, Nucl. Phys. B, 438 (1995) 109 [arXiv:hep-th/9410167].
34. FRE P., Lectures on Special Kahler Geometry and Electric-Magnetic Duality Rotations, Nucl. Phys. Proc. Suppl., 45BC (1996) 59 [arXiv:hep-th/9512043].
35. CREMMER È., JULIA B. L., LÜ H. and POPE C. N., Dualisation of Dualities, I & II, Nucl. Phys. B, 523 (1998) 73; 535 (1998) 242; [arXiv:hep-th/9710119], [arXiv:hep-th/9806106].
36. SCHWINGER J., A Magnetic Model of Matter, Science, 165 (1969) 757.
37. DE WIT B. and NICOLAI H., N=8 Supergravity, Nucl. Phys. B, 208 (1982) 323.
38. ANDRIANOPOLI L., D'AURIA R., FERRARA S. and LLEDO M. A., Gauging of flat groups in four dimensional supergravity, JHEP, 0207 (2002) 010 [arXiv:hep-th/0203206].
39. SCHERK J. and SCHWARZ J. H., How To Get Masses From Extra Dimensions, Nucl. Phys. B, 153 (1979) 61.
40. CREMMER E., SCHERK J. and SCHWARZ J. H., Spontaneously Broken N=8 Supergravity, Phys. Lett. B, 84 (1979) 83.
41. FERRARA S., KALLOSH R. and STROMINGER A., N=2 extremal black holes, Phys. Rev. D, 52 (1995) 5412 [arXiv:hep-th/9508072].
42. FERRARA S. and KALLOSH R., Supersymmetry and Attractors, Phys. Rev. D, 54 (1996) 1514 [arXiv:hep-th/9602136]; FERRARA S. and KALLOSH R., Universality of Supersymmetric Attractors, Phys. Rev. D, 54 (1996) 1525 [arXiv:hep-th/9603090].
43. STROMINGER A., Macroscopic Entropy of N = 2 Extremal Black Holes, Phys. Lett. B, 383 (1996) 39 [arXiv:hep-th/9602111].
44. BELLUCCI S., FERRARA S., KALLOSH R. and MARRANI A., Extremal Black Hole and Flux Vacua Attractors, [arXiv:hep-th/0711.4547].
45. ANDRIANOPOLI L., D'AURIA R., FERRARA S. and TRIGIANTE M., Extremal black holes in supergravity, Lect. Notes Phys., 737 (2008) 661 [arXiv:hep-th/0611345].
46. FERRARA S., HAYAKAWA K. and MARRANI A., Erice Lectures on Black Holes and Attractors, [arXiv:hep-th/0805.2498].
47. FERRARA S., GIBBONS G. W. and KALLOSH R., Black holes and critical points in moduli space, Nucl. Phys. B, 500 (1997) 75 [arXiv:hep-th/9702103].
48. KALLOSH R. and KOL B., E(γ) Symmetric Area of the Black Hole Horizon, Phys. Rev. D, 53 (1996) 5344 [arXiv:hep-th/9602014].
49. FERRARA S, and MALDACENA J. M., Branes, central charges and U-duality invariant BPS conditions, Class. Quantum Gravity, 15 (1998) 749 [arXiv:hep-th/9706097];
50. FERRARA S. and GUNAYDIN M., Orbits of exceptional groups, duality and BPS states in string theory, Int. J. Mod. Phys. A, 13 (1998) 2075 [arXiv:hep-th/9708025].
51. DESER S. and PUZALOWSKI R., Supersymmetric Nonpolynomial Vector Multiplets and Causal Propagation, J. Phys. A, 13 (1980) 2501.
52. CECOTTI S. and FERRARA S., Supersymmetric Born-Infeld Lagrangians, Phys. Lett. B, 187 (1987) 335.
53. BAGGER J. and GALPERIN A., A New Goldstone Multiplet for a Partially Broken Supersymmetry, Phys. Rev. D, 55 (1997) 1091; [arXiv:hep-th/9608177].
54. FREED D. S., Special Kaehler manifolds, Commun. Math. Phys., 203 (1999) 31 [arXiv:hep-th/9712042].
55. LLEDO M. A., MACIA O., VAN PROEYEN A. and VARADARAJAN V. S., Special geometry for arbitrary signatures, Contribution to the handbook on pseudo-Riemannian geometry and super-symmetry, edited by CORTÉS V., Eur. Math. Society series IRMA Lectures in Mathematics and Theoretical Physics. [arXiv:hep-th/0612210].
56. CORTES V., Special Kaehler manifolds: a survey, in Proceedings of the 21st Winter School on "Geometry and Physics" (Srni 2001), edited by SLOVAK J. and CADEK M., Rend. Circ. Mat. Palermo (2), Suppl. no. 66 (2001) 11, arXiv:math/0112114.
57. ASCHIERI P., Duality rotations and BPS monopoles with space and time noncommutativity, Nucl. Phys. B, 617 (2001) 321 [arXiv:hep-th/0106281].
58. ASCHIERI P., Monopoles in space-time noncommutative Born-Infeld theory, Fortsch. Phys., 50 (2002) 680 [arXiv:hep-th/0112186].
59. ASCHIERI P., CASTELLANI L. and ISAEV A. P., Discretized Yang-Mills and Born-Infeld actions on finite group geometries, Int. J. Mod. Phys. A, 18 (2003) 3555 [arXiv:hep-th/0201223].
60. BIALYNICKI-BIRULA I. and BIALYNICKA- BIRULA Z., Quantum Electrodynamics (Pergamon, Oxford) 1975 (also available at http://www.cft.edu.pl/~birula/publ.php).
61. DESER S. and TEITELBOIM C., Duality Transformations of Abelian and Nonabelian Gauge Fields, Phys. Rev. D, 13 (1976) 1592.
62. BIALYNICKI-BIRULA I., Nonlinear Electrodynamics: Variations on a Theme by Born and Infeld, In Quantum Theory of Particles and Fields, edited by JANCEWICZ B. and LUKIERSKI J., pp. 31-48 (also available at http://www.cft.edu.pl/~birula/publ.php).
63. DESER S. and SARIOGLU O., Hamiltonian electric/magnetic duality and Lorentz invariance, Phys. Lett. B, 423 (1998) 369 [arXiv:hep-th/9712067].
64. COLEMAN S. R., WESS J. and ZUMINO B., Structure of phenomenological Lagrangians. 1, Phys. Rev., 177 (1969) 2239.
65. CALLAN C. G., COLEMAN S. R., WESS J. and ZUMINO B., Structure of phenomenological Lagrangians. 2, Phys. Rev., 177 (1969) 2247.
66. ARGYRES P. C. and NAPPI C. R., Spin 1 Effective Actions from Open Strings, Nucl. Phys. B, 330 (1990) 151.
67. TSEYTLIN A. A., On Non-Abelian Generalisation of Born-Infeld Action in String Theory, Nucl. Phys. B, 501 (1997) 41; [arXiv:hep-th/9701125].
68. ANDRIANOPOLI L., D'AURIA R. and FERRARA S., U-invariants, black-hole entropy and fixed scalars, Phys. Lett. B, 403 (1997) 12 [arXiv:hep-th/9703156].
69. CASTELLANI L., CERESOLE A., FERRARA S., D'AURIA R., FRE P. and MAINA E., The Complete N = 3 Matter Coupled Supergravity, Nucl. Phys. B, 268 (1986) 317.
70. CREMMER E., in Supergravity '81, edited by FERRARA S. and TAYLOR J. G., p. 313;
71. JULIA B., in Superspace & Supergravity, edited by HAWKING S. and ROCEK M. (Cambridge University Press) 1981, p. 331.
72. KALLOSH R. and SOROUSH M., Explicit Action of E7(7) on N = 8 Supergravity Fields, Nucl. Phys. B, 801 (2008) 25 [arXiv:hep-th/0802.4106].
73. TRIGIANTE M., Dual Gauged Supergravities, [arXiv:hep-th/0701218].
74. CRAPS B., ROOSE F., TROOST W. and VAN PROEYEN A., What is special Kaehler geometry?, Nucl. Phys. B, 503 (1997) 565 [arXiv:hep-th/9703082].
75. ASCHIERI P. and SVRTAN D., Convergence of perturbative solutions of matrix equations, in preparation.
76. SCHWARZ A. S., Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem, Lett. Math. Phys., 52 (2000) 177 [arXiv:hep-th/0004088].
77. CERCHIAI B. L. and ZUMINO B., Properties of perturbative solutions of unilateral matrix equations, Lett. Math. Phys., 54 (2000) 33 [arXiv:hep-th/0009013];
78. CERCHIAI B. L. and ZUMINO B., Some remarks on unilateral matrix equations, Mod. Phys. Lett. A, 16 (2001) 191 [arXiv:hep-th/0105065].
79. ZUMINO B., Supersymmetry and Kahler Manifolds, Phys. Lett. B, 87 (1979) 203.
80. BINETRUY P. and GAILLARD M. K., S-Duality Constraints on Effective Potentials for Gaugino Condensation, Phys. Lett. B, 365 (1996) 87; [arXiv:hep-th/9506207].
81. ANDRIANOPOLI L., D'AURIA R., FERRARA S. and TRIGIANTE M., Black-hole attractors in N = 1 supergravity, JHEP, 0707 (2007) 019 [arXiv:hep-th/0703178].
82. FERRARA S. and STROMINGER A., N = 2 space-time supersymmetry and Calabi Yau Moduli Space, in Proceedings of College Station Workshop "Strings '89", edited by ARNOWITT et al. (World scientific) 1989, p. 245;
83. CANDELAS P. and DE LA OSSA X., Moduli Space of Calabi Yau Manifolds, Nucl. Phys. B, 355 (1991) 455;
84. DE WIT B. and VAN PROEYEN A., Potentials and Symmetries of General Gauged N = 2 Supergravity - Yang-Mills Models, Nucl. Phys. B, 245 (1984) 89;
85. CREMMER'E., KOUNNAS C., VAN PROEYEN A., DERENDINCER J. P., FERRARA S., DE WIT B, and GIRARDELLO L., Vector Multiplets Coupled to N = 2 Supergravity: Superhiggs Effect, Flat Potentials and Geometric Structure, Nucl. Phys. B, 250 (1985) 385;
86. DE WIT B., LAUWERS P. G. and VAN PROEYEN A., Lagrangians of N = 2 Supergravity - Matter Systems, Nucl. Phys. B, 255 (1985) 569;
87. FERRARA S., KOUNNAS C., LUST D. and ZWIRNER F., Duality invariant partition functions and automorphic superpotentials for (2, 2) string compactifications, Nucl. Phys. B, 365 (1991) 431;
88. CASTELLANI L., D'AURIA R. and FERRARA S., Special geometry without special coordinates, Class. Quantum. Gravity, 7 (1990) 1767;
89. CASTELLANI L., D'AURIA R. and FERRARA S., Special Kahler Geometry; an intrinsic Formulation from N = 2 Space-Time Supersymmetry, Phys. Lett. B, 241 (1990) 57.
90. STROMINGER A., Special Geometry, Commun. Math. Phys., 133 (1990) 163.
91. ANDRIANOPOLI L., BERTOLINI M., CERESOLE A., D'AURIA R., FERRARA S., FRÉ P. and MAGRI T., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys., 23 (1997) 111 [arXiv:hep-th/9605032];
92. ANDRIANOPOLI L., BERTOLINI M., CERESOLE A., D'AURIA R., FERRARA S. and FRÉ P., General Matter Coupled N = 2 Supergravity, Nucl. Phys. B, 476 (1996) 397 [arXiv:hep-th/9603004].
93. CREMMER E. and VAN PROEYEN A., Classification of Kahler Manifolds in N = 2 Vector Multiplet Supergravity Couplings, Class. Quantum Gravity, 2 (1985) 445.
94. SEIBERG N. and WITTEN E., String theory and noncommutative geometry, JHEP, 9909 (1999) 032 [arXiv:hcp-th/9908142] .
95. MADORE J., SCHRAML S., SCHUPP P. and WESS J., Gauge theory on noncommutative spaces, Eur. Phys. J. C, 16 (2000) 161 [arXiv:hep-th/0001203].
96. JURCO B., SCHUPP P. and WESS J., Nonabelian noncommutative gauge theory via noncommutative extra dimensions, Nucl. Phys. B, 604 (2001) 148 [arXiv:hep-th/0102129].
97. SEIBERG N., SUSSKIND L. and TOUMBAS N., Space/time non-commutativity and causality, JHEP, 0006 (2000) 044 [arXiv:hep-th/0005015];
98. BARBON J. L. and RABINOVICI E., Stringy fuzziness as the custodian of time-space noncommutativity, Phys. Lett. B, 486 (2000) 202 [arXiv:hep-th/0005073];
99. GOMIS J. and MEHEN T., Space-time noncommutative field theories and unitarity, Nucl. Phys. B, 591 (2000) 265 [arXiv:hep-th/0005129].
100. AHARONY O., GOMIS J. and MEHEN T., On theories with light-like noncommutativity, JHEP, 0009 (2000) 023 [arXiv:hep-th/0006236].
101. BAHNS D., DOPLICHER S., FREDENHAGEN K. and PIACITELLI G., On the unitarity problem in space/time noncommutative theories, Phys. Lett. B, 533 (2002) 178 [arXiv:hep-th/0201222].
102. ASCHIERI P., On duality rotations in light-like noncommutative electromagnetism, Mod. Phys. Lett. A, 16 (2001) 163 [arXiv:hep-th/0103150].
103. GANOR O. J., RAJESH G. and SETHI S., Duality and non-commutative gauge theory, Phys. Rev. D, 62 (2000) 125008 [arXiv:hep-th/0005046].
104. GOPAKUMAR R., MALDACENA J., MINWALLA S. and STROMINGER A., S-duality and noncommutative gauge theory, JHEP, 0006 (2000) 036 [arXiv:hep-th/0005048].
105. REY S. and VON UNGE R., S-duality, noncritical open string and noncommutative gauge theory, Phys. Lett. B, 499 (2001) 215 [arXiv:hep-th/0007089].
106. LU J. X., ROY S. and SINGH H., SL(2, Z) duality and 4-dimensional noncommutative theories, Nucl. Phys. B, 595 (2001) 298 [arXiv:hep-th/0007168].
107. ALISHAHIHA M., OZ Y. and RUSSO J. G., Supergravity and light-like non-commutativity, JHEP, 0009 (2000) 002 [arXiv:hep-th/0007215].
108. SCHWARZ A., Morita equivalence and duality, Nucl. Phys. B, 534 (1998) 720 [arXiv:hep-th/9805034];
109. HO P., Twisted bundle on quantum torus and BPS states in matrix theory, Phys. Lett. B, 434 (1998) 41 [arXiv:hep-th/9803166];
110. BRACE D., MORARIU B. and ZUMINO B., Dualities of the matrix model from T-duality of the type II string, Nucl. Phys. B, 545 (1999) 192 [arXiv:hep-th/9810099].
111. CHU C. and HO P., Noncommutative open string and D-brane, Nucl. Phys. B, 550 (1999) 151 [arXiv:hep-th/9812219].