High Energy Theory Seminar

We give a full list of known N=1 supersymmetric quantum field theories related by the Seiberg duality conjectures for the SU(N), SP(2N) and G_2 gauge groups. There are both new dualities and new theories with confinement, not considered earlier in the literature. For all these N=1 theories we construct superconformal indices and express them in terms of elliptic hypergeometric integrals. Equality of indices in dual theories leads to various identities for elliptic hypergeometric integrals. About half of them was proven earlier, and another half represents new challenging conjectures. In particular, we conjecture a dozen of new elliptic beta integrals on root systems. Also for the special N=1 SYM theory with SP(2N) gauge group and 8 flavours we conjecture the existence of 72 dual theories, which can be explained through the action of the coset group W(E_7)/S_8 where W(E_7) is the Weyl group of the exceptional root system E_7. The talk is based on two papers in collaboration with Vyacheslav Spiridonov: arXiv:0811.1909 and arXiv:0910.5944.