Nekrasov prepotential with fundamental matter from the quantum spin chain

Abstract

Nekrasov functions were conjectured in \cite{Mironov:2009uv} to be related to exact Bohr-Sommerfeld periods of quantum integrable systems. This statement was thoroughly checked for the case of the pure $SU(N_c)$ gauge theory in \cite{Mironov:2009dv} and \cite{Popolitov:2010bz}. Here we successfully perform a set of checks in the case of gauge group $SU(N_c)$ with additional $N_f$ fundamental hypermultiplets. We show that the Baxter equation for the spin chain gives the same quantum periods as the one for the Gaudin system in this case.

13 pages, 1 figure, added reference

References in corpus (12)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• The Coulomb Phase of N=2 Supersymmetric QCD
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• The Effective Prepotential of N=2 Supersymmetric SU(N_c) Gauge Theories
• N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_c
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants

Cited by in corpus (34)

• Proving AGT conjecture as HS duality: extension to five dimensions
• QNMs of branes, BHs and fuzzballs from Quantum SW geometries
• Spectral Duality Between Heisenberg Chain and Gaudin Model
• Quantization of Integrable Systems and a 2d/4d Duality
• Black hole perturbation theory and multiple polylogarithms
• Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
• A slow review of the AGT correspondence
• S-duality as a beta-deformed Fourier transform
• Exact WKB methods in $SU(2)$ $N_f=1$
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Three-particle Integrable Systems with Elliptic Dependence on Momenta and Theta Function Identities
• Quasinormal Modes of C-metric from SCFTs
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• Quantum Seiberg-Witten curve and Universality in Argyres-Douglas theories
• An alternative to the Teukolsky equation
• Confinement and Mayer cluster expansions
• Quantum spectral problems and isomonodromic deformations
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential
• Quantum periods for $\mathcal{N}=2$ $SU(2)$ SQCD around the superconformal point
• Challenges of beta-deformation
• Quantum Seiberg-Witten periods for $\mathcal{N}=2$ $SU(N_c)$ SQCD around the superconformal point
• Notes on Mayer Expansions and Matrix Models
• Quantum periods and TBA equations for $\mathcal{N}=2SU(2)N_f=2$ SQCD with flavor symmetry
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• Quantum spectral curve for (q,t)-matrix model
• More on the SW-QNM correspondence
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• Painlevé Kernels and Surface Defects at Strong Coupling
• On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain