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Superconformal Indices of \({{\mathcal N}=4}\) SYM Field Theories

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Abstract

Superconformal indices (SCIs) of 4d \({{\mathcal N} = 4}\) SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For F 4, E 6, E 7, E 8 gauge groups this yields first examples of integrals of such type. S-duality transformation for G 2 and F 4 SCIs is equivalent to a change of integration variables. Equality of SCIs for SP(2N) and SO(2N + 1) group theories is proved in several important special cases. Reduction of SCIs to partition functions of 3d \({{\mathcal N}=2}\) SYM theories with one matter field in the adjoint representation is investigated, corresponding 3d dual partners are found, and some new related hyperbolic beta integrals are conjectured.

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Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Moscow Region, 141980, Russia

    Vyacheslav P. Spiridonov

  2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Vyacheslav P. Spiridonov

  3. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, 14476, Golm, Germany

    Grigory S. Vartanov

Authors
  1. Vyacheslav P. Spiridonov
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  2. Grigory S. Vartanov
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Correspondence to Grigory S. Vartanov.

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Spiridonov, V.P., Vartanov, G.S. Superconformal Indices of \({{\mathcal N}=4}\) SYM Field Theories. Lett Math Phys 100, 97–118 (2012). https://doi.org/10.1007/s11005-011-0537-2

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