Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings

TL;DR

This paper explores the spectral dualities connecting elliptic integrable systems, gauge theories in higher dimensions, and topological string amplitudes, revealing deep mathematical structures and symmetries.

Contribution

It establishes a correspondence between topological string amplitudes, elliptic and affine Selberg integrals, and 5D/6D gauge theories, highlighting spectral dualities and their relation to integrable systems.

Findings

Spectral duality between XYZ spin chain and Ruijsenaars system.

Connection between topological string amplitudes and elliptic Selberg integrals.

Self-duality of the double elliptic system.

Abstract

We consider Dotsenko-Fateev matrix models associated with compactified Calabi-Yau threefolds. They can be constructed with the help of explicit expressions for refined topological vertex, i.e. are directly related to the corresponding topological string amplitudes. We describe a correspondence between these amplitudes, elliptic and affine type Selberg integrals and gauge theories in five and six dimensions with various matter content. We show that the theories of this type are connected by spectral dualities, which can be also seen at the level of elliptic Seiberg-Witten integrable systems. The most interesting are the spectral duality between the XYZ spin chain and the Ruijsenaars system, which is further lifted to self-duality of the double elliptic system.