Mathematical Physics and String Theory

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Elliptic hypergeometric integrals and 4d superconformal index

Grigory Vartanov (DESY)

05.07.2012 at 16:15

I will describe superconformal indices of four-dimensional supersymmetric gauge field theories which are given in terms of elliptic hypergeometric integrals-- the top known level of special functions of hypergeometric type. Superconformal indices of theories related by the Seiberg duality coincide as a consequence of nontrivial identities for corresponding integrals. In the talk it will be shown that 't Hooft anomaly matching conditions for dual theories are related to SL(3,Z) modular transformation properties of the kernels of dual indices. Application of this technique to theories with chiral symmetry breaking is illustrated. Apart from 4d interpretation there is connection to partition functions of lower dimensional supersymmetric field theories (this is a joint work with V. P. Spiridonov).

Arnold Sommerfeld Center
Theresienstrasse 37
Room 348/349