Deformed SW curve and the null vector decoupling equation in Toda field theory

Abstract

It is shown that the deformed Seiberg-Witten curve equation after Fourier transform is mapped into a differential equation for the AGT dual 2d CFT cnformal block containing an extra completely degenerate field. We carefully match parameters in two sides of duality thus providing not only a simple independent prove of the AGT correspondence in Nekrasov-Shatashvili limit, but also an extension of AGT to the case when a secondary field is included in the CFT conformal block. Implications of our results in the study of monodromy problems for a large class of $n$'th order Fuchsian differential equations are discussed.

references added, published version

References in corpus (8)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Non-perturbative studies of N=2 conformal quiver gauge theories
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Irregular conformal block, spectral curve and flow equations

Cited by in corpus (1)

• Quantum Seiberg-Witten curve and Universality in Argyres-Douglas theories