N=2 supersymmetric QCD and elliptic potentials

Abstract

We investigate the relation between the four dimensional N=2 SU(2) super Yang-Mills theory with four fundamental flavors and the quantum mechanics model with Treibich-Verdier potential described by the Heun equation in the elliptic form. We study the precise correspondence of quantities in the gauge theory and the quantum mechanics model. An iterative method is used to obtain the asymptotic expansion of the spectrum for the Schrödinger operator, we are able to fix the precise relation between the energy spectrum and the instanton partition function of the gauge theory. We also study asymptotic expansions for the spectrum which correspond to the strong coupling regions of the Seiberg-Witten theory.

Latex, 29pp, published version, content restructured and simplified

References in corpus (7)

• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• Transformations of Spherical Blocks
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants
• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

Cited by in corpus (6)

• A slow review of the AGT correspondence
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations
• A new treatment for some periodic Schrödinger operators I: the eigenvalue
• Spectra of elliptic potentials and supersymmetric gauge theories
• Properties of some elliptic Hill's potentials