Ground state wavefunctions of elliptic relativistic integrable Hamiltonians

TL;DR

This paper derives ground state eigenfunctions and eigenvalues for relativistic elliptic integrable models relevant to superconformal index computations, using physical dualities and assumptions about compactification limits.

Contribution

It provides explicit derivations of ground state wavefunctions for elliptic relativistic integrable models, connecting physical dualities with mathematical solutions.

Findings

Eigenfunctions for Ruijsenaars-Schneider and van Diejen models derived

Connections established between integrable models and superconformal indices

Method relies on physical dualities and compactification limits

Abstract

We derive ground state eigenfunctions and eigenvalues of various relativistic elliptic integrable models. The models we discuss appear in computations of superconformal indices of four-dimensional theories obtained by compactifying six-dimensional models on Riemann surfaces. These include, among others, the Ruijsenaars-Schneider model and the van Diejen model. The derivation of the eigenfunctions builds on physical inputs, such as conjectured Lagrangian across dimensions IR dualities and assumptions about the behavior of the indices in the limit of compactifications on surfaces with large genus/number of punctures/flux.