# Aspects of elliptic hypergeometric functions

@article{Spiridonov2013AspectsOE, title={Aspects of elliptic hypergeometric functions}, author={Vyacheslav Pavlovich Spiridonov}, journal={arXiv: Classical Analysis and ODEs}, year={2013} }

General elliptic hypergeometric functions are defined by elliptic hypergeometric integrals. They comprise the elliptic beta integral, elliptic analogues of the Euler-Gauss hypergeometric function and Selberg integral, as well as elliptic extensions of many other plain hypergeometric and $q$-hypergeometric constructions. In particular, the Bailey chain technique, used for proving Rogers-Ramanujan type identities, has been generalized to integrals. At the elliptic level it yields a solution of… Expand

#### 7 Citations

Elliptic hypergeometric functions

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Lecture notes for a course given at the summer school OPSF-S6, College Park, Maryland, 11-15 July 2016. In these lecture notes I give an elementary introduction to elliptic hypergeometric functions.… Expand

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We consider 4d supersymmetric (special) unitary $\Gamma$ quiver gauge theories on compact manifolds which are $T^2$ fibrations over $S^2$. We show that their partition functions are correlators of… Expand

A new pentagon identity for the tetrahedron index

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A bstractRecently Kashaev, Luo and Vartanov, using the reduction from a fourdimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special… Expand

Superconformal indices, dualities and integrability

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In this thesis we discuss exact, non-perturbative results achieved using superconformal index technique in supersymmetric gauge theories with four supercharges (which is N = 1 supersymmetry in four… Expand

Quiver gauge theories and integrable lattice models

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A bstractWe discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The… Expand

Flavored surface defects in 4d $$\mathcal{N}=1$$N=1 SCFTs

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We discuss supersymmetric surface defects in compactifications of six-dimensional minimal conformal matter of types SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions… Expand

Flavored surface defects in 4d N=1 SCFTs

- Physics
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We discuss supersymmetric surface defects in compactifications of six dimensional minimal conformal matter of type SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions… Expand

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