Superconformal indices of ${\mathcal N}=4$ SYM field theories

Details Superconformal indices of ${\mathcal N}=4$ SYM field theories Superconformal indices of ${\mathcal N}=4$ SYM field theories

2010-05-23

arxiv.org/abs/1005.4196v3

Physics

High Energy Physics

High Energy Physics - Theory

19 pages; v. 2: a substantially improved version; v. 3: the paper was shortened by the demand of a Referee. New results on the

Scientific paper

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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