Deformed planar topological open string amplitudes on Seiberg-Witten curve

TL;DR

This paper explores refined B-model topological string amplitudes on Seiberg-Witten curves for N=2 SU(2) gauge theories with various flavors, establishing links with Nekrasov-Shatashvili limits and AGT correspondence.

Contribution

It provides a detailed analysis of deformed disk and annulus amplitudes on Seiberg-Witten curves and connects them with irregular conformal blocks via the AGT correspondence.

Findings

Confirmed agreement between deformed amplitudes and irregular blocks for N_f=0 and 1.

Established correspondence between deformed disk amplitudes and Nekrasov-Shatashvili limit.

Analyzed relations between deformed annulus amplitudes and irregular two-point blocks.

Abstract

We study refined B-model via the beta ensemble of matrix models. Especially, for four dimensional N=2 SU(2) supersymmetric gauge theories with N_f=0,1 and 2 fundamental flavors, we discuss the correspondence between deformed disk amplitudes on each Seiberg-Witten curve and the Nekrasov-Shatashvili limit of the corresponding irregular one point block of a degenerate operator via the AGT correspondence. We also discuss the relation between deformed annulus amplitudes and the irregular two point block of the degenerate operator, and check a desired agreement for N_f=0 and 1 cases.