# Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory

## TL;DR

This paper develops an exact method for solving the quantum relativistic Toda chain using Separation of Variables and gauge theory, incorporating non-perturbative corrections and modular duality to determine energy spectra.

## Contribution

It introduces a gauge theory-based approach with codimension two defects on curved backgrounds to construct exact eigenfunctions and spectra for the relativistic Toda chain.

## Key findings

- Successful construction of exact eigenfunctions
- Inclusion of non-perturbative quantum corrections
- Validation against numerical results

## Abstract

We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the $N$-particle relativistic Toda chain and test our proposal against numerical results. Quantum Mechanical non-perturbative corrections, essential in order to obtain a sensible solution, are taken into account in our gauge theory approach by considering codimension two defects on curved backgrounds (squashed $S^5$ and degenerate limits) rather than flat space; this setting also naturally incorporates exact quantization conditions and energy spectrum of the relativistic Toda chain as well as its modular dual structure.