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 \( \mathcal{N}={1}^{\ast } \) 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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Hatsuda, Y., Sciarappa, A. & Zakany, S. Exact quantization conditions for the elliptic Ruijsenaars-Schneider model. J. High Energ. Phys. 2018, 118 (2018). https://doi.org/10.1007/JHEP11(2018)118
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DOI: https://doi.org/10.1007/JHEP11(2018)118