Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories

摘要

The results of Romelsberger for a N=1 superconformal index counting protectedoperators, satisfying a BPS condition and which cannot be combined to form longmultiplets, are analysed further. The index is expressible in terms of singleparticle superconformal characters for N=1 scalar and vector multiplets. ForSQCD, 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 resultsfor theories linked by Seiberg duality using recently proved theorems forq-series elliptic hypergeometric integrals. The discussion is also extended toKutasov-Schwimmer dual theories in the large N_c, N_f limit and to dualtheories with Sp(N) and SO(N) gauge groups. For the former, a transformationidentity for elliptic hypergeometric integrals directly verifies that the indexis the same for the electric and magnetic theories. For SO(N) theories thecorresponding result may also be obtained from the same basic identity. Anexpansion of the index to several orders is also obtained in a form where thedetailed protected operator content may be read off. Relevant mathematicalresults are reviewed.