Mathematical structures behind supersymmetric dualities

Ilmar Gahramanov

Particle Physics Research Group, Institute of Radiation Problems, Azerbaijan National Academy of Sciences, B.Vahabzade 9, AZ1143 Baku, Azerbaijan
Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Grossen Windkanal 6, D12489 Berlin, Germany


Abstract: The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.

AMSclassification: primary 81T60; secondary 33D60, 33E20, 33D90, 39A13.

Keywords: elliptic hypergeometric function, hypergeometric series on root systems, basic hypergeometric integrals, hyperbolic hypergeometric integrals, superconformal index, supersymmetric duality, Seiberg duality, mirror symmetry.

DOI: 10.5817/AM2015-5-273