Constructs solutions to higher-rank oper Riemann-Hilbert problems via a single non-linear integral equation, proving that the oper generating function equals the Toda Yang-Yang function and thereby establishing the Nekrasov-Rosly-Shatashvili conjecture.
Exact quantization conditions for the elliptic Ruijsenaars-Schneider model
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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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Generalized Schur indices of N=2 class S theories are expressed using eigenfunctions of non-relativistic elliptic Calogero-Moser models, with extensions claimed for N=1 SCFTs via limits of models like Inozemtsev.
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Higher-Rank Mathieu Opers, Toda Chain, and Analytic Langlands Correspondence
Constructs solutions to higher-rank oper Riemann-Hilbert problems via a single non-linear integral equation, proving that the oper generating function equals the Toda Yang-Yang function and thereby establishing the Nekrasov-Rosly-Shatashvili conjecture.
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On non-relativistic integrable models and 4d SCFTs
Generalized Schur indices of N=2 class S theories are expressed using eigenfunctions of non-relativistic elliptic Calogero-Moser models, with extensions claimed for N=1 SCFTs via limits of models like Inozemtsev.