Superconformal indices of ${\mathcal N}=4$ SYM field theories
Abstract
Superconformal indices (SCIs) of 4d SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For 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 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.
Cite
@article{arxiv.1005.4196,
title = {Superconformal indices of ${\mathcal N}=4$ SYM field theories},
author = {V. P. Spiridonov and G. S. Vartanov},
journal= {arXiv preprint arXiv:1005.4196},
year = {2015}
}
Comments
19 pages; v. 2: a substantially improved version; v. 3: the paper was shortened by the demand of a Referee. New results on the reduction of 4d indices to 3d partition functions are added. Version to appear in Lett. Math. Phys