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

Jan, 2008
47 pages
Published in:
  • Nucl.Phys.B 818 (2009) 137-178
e-Print:
Report number:
  • DAMTP-08-07,
  • DIAS-STP-08-02,
  • SHEP-08-06

Citations per year

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Abstract: (Elsevier)
The results of Römelsberger for an 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 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.
Note:
  • 47 pages, uses harvmac, v2. minor corrections, SO(N) cases proved, ref. added, v3. minor additions and corrections
  • N = 1 superconformal symmetry
  • Seiberg duality
  • Characters
  • Superconformal index
  • q-series
  • N = 1 superconformal symmetry
  • q -series
  • [formula omitted] superconformal symmetry
  • supersymmetry
  • index theorem