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

The results of Romelsberger for in N = 1 superconformal index counting protected operators, satisfying a BPS condition and which cannot be combined to form long multiplets, are analysed further. The index is expressible in terms of single particle superconformal characters for N = 1 scalar and vector multiplets. For SQCD, involving SU(N-c) gauge groups and appropriate numbers of flavours N-f, the formula used to construct the index may be proved to give identical results for theories linked by Seiberg duality using recently proved theorems for q-series elliptic hypergeometric integrals. The discussion is also extended to Kutasov-Schwimmer dual theories in the large N-c, N-f limit and to dual theories with S-p(N) and SO(N) gauge groups. For the former, a transformation identity for elliptic hypergeometric integrals directly verifies that the index is the same for the electric and magnetic theory. For SO(N) theories the corresponding result may also,be-obtained from the same basic identity. An expansion of the index to several orders is also obtained-in a form where the detailed protected operator content may be read off. Relevant mathematical results are reviewed. (C) 2009 Elsevier B.V. All rights reserved.