Refined Cigar and Omega-deformed Conifold

TL;DR

This paper explores the relationship between Omega-deformation and refined topological string theory on the deformed conifold, using a non-compact Gepner model approach to confirm theoretical predictions.

Contribution

It demonstrates the correspondence between refined correlation functions in a Kazama-Suzuki coset model and c=1 non-critical string theory interpretations for the deformed conifold.

Findings

Refined correlation functions match c=1 string theory predictions.

Agreement with the Omega-deformation proposal after subtracting singularities.

Provides a non-compact Gepner model perspective on the deformed conifold.

Abstract

Antoniadis et al proposed a relation between the Omega-deformation and refined correlation functions of the topological string theory. We investigate the proposal for the deformed conifold geometry from a non-compact Gepner model approach. The topological string theory on the deformed conifold has a dual description in terms of the c=1 non-critical string theory at the self-dual radius, and the Omega-deformation yields the radius deformation. We show that the refined correlation functions computed from the twisted SL(2,R)/U(1) Kazama-Suzuki coset model at level k=1 have direct c=1 non-critical string theory interpretations. After subtracting the leading singularity to procure the 1PI effective action, we obtain the agreement with the proposal.