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

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.

arXiv comment85 pages, 6 tables, 21 figures

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• BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves
• Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model
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