Applications of the superconformal index for protected operators and q-hypergeometric identities to N = 1 dual theories

Nuclear Physics B

Volumn 818, Issue 3, 2009, Pages 137-178

  Dolan, F A ^a,b   Osborn, H ^c  

^a DUBLIN INSTITUTE FOR ADVANCED STUDIES   (Ireland)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Characters; N = 1 superconformal symmetry; q series; Seiberg duality; Superconformal index

Indexed keywords

EID: 67349170772     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2009.01.028     Document Type: Article

References (31)

1. Seiberg N. Electric-magnetic duality in supersymmetric non-Abelian gauge theories. Nucl. Phys. B 435 (1995) 129. hep-th/9411149
2. Terning J. Modern Supersymmetry (2006), Clarendon Press, Oxford
3. c) gauge theories. Nucl. Phys. B 448 (1995) 187. hep-th/9505051
4. Kutasov D. A comment on duality in N = 1 supersymmetric non-Abelian gauge theories. Phys. Lett. B 351 (1995) 230. hep-th/9503086
5. Kutasov D., and Schwimmer A. On duality in supersymmetric Yang-Mills theory. Phys. Lett. B 354 (1995) 315. hep-th/9505004
6. Kutasov D., Schwimmer A., and Seiberg N. Chiral rings, singularity theory and electric-magnetic duality. Nucl. Phys. B 459 (1996) 455. hep-th/9510222
7. Kinney J., Maldacena J.M., Minwalla S., and Raju S. An index for 4-dimensional super-conformal theories. Commun. Math. Phys. 275 (2007) 209. hep-th/0510251
8. Janik R.A., and Trzetrzelew M. Supergravitons from one loop perturbative N = 4 SYM. arXiv:0712.2714 [hep-th]
9. Bianchi M., Dolan F.A., Heslop P.J., and Osborn H. N = 4 superconformal characters and partition functions. Nucl. Phys. B 767 (2007) 163. hep-th/0609179
10. Römelsberger C. Counting chiral primaries in N = 1, d = 4 superconformal field theories. Nucl. Phys. B 747 (2006) 329. hep-th/0510060
11. Römelsberger C. Calculating the superconformal index and Seiberg duality. arXiv:0707.3702 [hep-th]
12. Feng B., Hanany A., and He Y.H. Counting gauge invariants: The plethystic program. JHEP 0703 (2007) 090. hep-th/0701063
13. Pouliot P. Molien function for duality. JHEP 9901 (1999) 021. hep-th/9812015
14. Nassrallah B., and Rahman M. Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials. SIAM J. Math. Anal. 16 (1985) 186
15. 9 rational functions. Can. J. Math. 38 (1986) 605
16. Spiridonov V.P. On the elliptic beta function. Russian Math. Surv. 56 (2001) 185
17. Spiridonov V.P. An elliptic beta integral. In: Elaydi S. (Ed). Proceedings of the Fifth International Conference on Difference Equations (2002), Taylor & Francis, London
18. E.M. Rains, Transformations of elliptic hypergeometric integrals, math/0309252, Ann. Math., in press
19. Dolan F.A. Counting BPS operators in N = 4 SYM. Nucl. Phys. B 790 (2008) 432. arXiv:0704.1038 [hep-th]
20. Gasper G., and Rahman M. Basic Hypergeometric Series (2004), Cambridge Univ. Press, Cambridge
21. Askey R. Beta Integrals in Ramanujan's Papers, Ramanujan Revisited (1988), Academic Press, London pp. 561-590
22. Spiridonov V.P. Short proofs of elliptic beta integrals. Ramanujan J. 13 (2007) 265. math.CA/0408369
23. Rains E.M., and Spiridonov V.P. Determinants of elliptic hypergeometric integrals. arXiv:0712.4253 [math.CA]
24. c) gauge theories. Phys. Lett. B 353 (1995) 471. hep-th/9505006
25. c) gauge theories. Nucl. Phys. B 444 (1995) 125. hep-th/9503179
26. E.M. Rains, private communication
27. Spiridonov V.P. In: Noumi M., and Takasaki K. (Eds). Classical Elliptic Hypergeometric Functions and Their Applications. Rokko Lectures in Mathematics vol. 18 (2005), Elliptic Integrable Systems. math.CA/0511579
28. Distler J., and Karch A. N = 1 dualities for exceptional gauge groups and quantum global symmetries. Fortschr. Phys. 45 (1997) 517. hep-th/9611088
29. Karch A. More on N = 1 dualities and exceptional gauge groups. Phys. Lett. B 405 (1997) 280. hep-th/9702179
30. Dolan F.A., and Osborn H. On short and semi-short representations for four-dimensional superconformal symmetry. Ann. Phys. 307 (2003) 41. hep-th/0209056
31. Dolan F.A. Character formulae and partition functions in higher dimensional conformal field theory. J. Math. Phys. 47 (2006) 062303. hep-th/0508031