Introduction to the Theory of Elliptic Hypergeometric Integrals

Lectures on the Superconformal Index

“…In fact the integrals of these types, called the elliptic hypergeometric integrals, have been studied separately by mathematicians. See [22] for an introduction and references. More importantly from a physicists point of view, matching of superconformal index provides a non-trivial check on remarkable non-perturbative duality conjectures.…”

Selberg integrals of Alba–Fateev–Litvinov–Tarnopolsky type

“…Much of the theory of qhypergeometric series and integrals extends naturally to the elliptic level. For an introduction to the theory of elliptic hypergeometric functions see [GR04,Ros,Spi]. The primary building block of the elliptic theory is the modified theta function Â.zI q; p/ WD .zI p/ 1 .p=zI p/ 1 ;…”