Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-01-31
Nucl.Phys.B818:137-178,2009
Physics
High Energy Physics
High Energy Physics - Theory
47 pages, uses harvmac, v2. minor corrections, SO(N) cases proved, ref. added, v3. minor additions and corrections
Scientific paper
10.1016/j.nuclphysb.2009.01.028
The results of Romelsberger for a 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 Sp(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 theories. 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.
Dolan Francis A.
Osborn Herbert
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