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arXiv · 1809.10294

Exact quantization conditions for the elliptic Ruijsenaars-Schneider model

Yasuyuki Hatsuda·Antonio Sciarappa·Szabolcs Zakany
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Abstract

We propose and test exact quantization conditions for the $N$-particle quantum elliptic Ruijsenaars-Schneider integrable system, as well as its Calogero-Moser limit, based on the conjectural correspondence to the five-dimensional $\mathcal{N} = 1$ $SU(N)$ gauge theory in the Nekrasov-Shatashvili limit. We discuss two natural sets of quantization conditions, related by the electro-magnetic duality, and the importance of non-perturbative corrections in the Planck constant. We also comment on the eigenfunction problem, by reinterpreting the Separation of Variables approach in gauge theory terms.

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Yasuyuki Hatsuda, Antonio Sciarappa, Szabolcs Zakany. 2018-09-27. Exact quantization conditions for the elliptic Ruijsenaars-Schneider model. https://doi.org/10.1007/jhep11(2018)118

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