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arXiv · 2407.08776

On Ruijsenaars-Schneider spectrum from superconformal indices and ramified instantons

Hee-Cheol Kim·Anton Nedelin·Shlomo S. Razamat
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Abstract

We discuss two physics-inspired approaches to derivation of the eigenfunctions and eigenvalues of $A_N$ Ruijsenaars-Schneider model. First approach which was recently proposed by the authors relies on the computations of superconformal indices of class $\mathcal{S}$ $4d$ ${\mathcal N}=2$ theories with the insertion of surface defects. Second approach uses computations of Nekrasov-Shatashvili limit of $5d$ ${\mathcal N} = 1^*$ instanton partition functions in the presence of co-dimension two defect. We compare results of these two approaches for the low-lying levels of Ruijsenaars-Schneider model. We also discuss different previously proposed exact quantization conditions for the Coulomb branch parameters of the instanton partition functions and their interpretations in terms of index calculations.

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Hee-Cheol Kim, Anton Nedelin, Shlomo S. Razamat. 2024-07-11. On Ruijsenaars-Schneider spectrum from superconformal indices and ramified instantons. https://arxiv.org/abs/2407.08776

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