Exact quantization conditions for the elliptic Ruijsenaars-Schneider model

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.

arXiv comment50 pages + appendices, 13 tables

References in corpus (38)

• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Discrete Heisenberg-Weyl Group and Modular Group
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• M5-branes from gauge theories on the 5-sphere
• Supersymmetric Gauge Theories on the Five-Sphere
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Defects and Quantum Seiberg-Witten Geometry
• Twisted supersymmetric 5D Yang-Mills theory and contact geometry
• Affine SL(2) conformal blocks from 4d gauge theories
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Instanton counting with a surface operator and the chain-saw quiver
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• Perturbative partition function for a squashed S^5
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• 5d Partition Functions with A Twist
• Topological Strings and Quantum Spectral Problems
• Line defects and 5d instanton partition functions
• Exact quantization conditions for the relativistic Toda lattice
• Supersymmetric theories on squashed five-sphere
• Exact quantization conditions for cluster integrable systems
• Eigenfunctions of $GL(N,\RR)$ Toda chain: The Mellin-Barnes representation
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Quantization condition from exact WKB for difference equations
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Wilson surfaces in M5-branes
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type IV. The Relativistic Heun (van Diejen) Case
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Combinatorial approach to Mathieu and Lamé equations
• An explicit solution of the (quantum) elliptic Calogero-Sutherland model
• Solution of Baxter equation for the $q$-Toda and Toda${}_2$ chains by NLIE

Cited by in corpus (4)

• Exact WKB methods in $SU(2)$ $N_f=1$
• Quantum spectral problems and isomonodromic deformations
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• Spectra of elliptic potentials and supersymmetric gauge theories