Worldsheet Realization of the Refined Topological String

TL;DR

This paper proposes a worldsheet approach to the refined topological string, connecting string amplitudes with Nekrasov partition functions and identifying deformation parameters with specific field-strength backgrounds.

Contribution

It introduces a novel worldsheet realization of the refined topological string that reproduces Nekrasov partition functions and clarifies the role of deformation parameters in string theory.

Findings

Exact one-loop string amplitude computations match Nekrasov partition functions.

Deformation parameters epsilon_- and epsilon_+ correspond to specific field-strength backgrounds.

The approach applies to Heterotic and Type I theories on K3xT2.

Abstract

A worldsheet realization of the refined topological string is proposed in terms of physical string amplitudes that compute generalized N=2 F-terms of the form F_{g,n} W^{2g}Y^{2n} in the effective supergravity action. These terms involve the chiral Weyl superfield W and a superfield Y defined as an N=2 chiral projection of a particular anti-chiral T-bar vector multiplet. In Heterotic and Type I theories, obtained upon compactification on the six-dimensional manifold K3xT2, T is the usual K\"ahler modulus of the T2 torus. These amplitudes are computed exactly at the one-loop level in string theory. They are shown to reproduce the correct perturbative part of the Nekrasov partition function in the field theory limit when expanded around an SU(2) enhancement point of the string moduli space. The two deformation parameters epsilon_- and epsilon_+ of the Omega-supergravity background are then identified with the constant field-strength backgrounds for the anti-self-dual graviphoton and self-dual gauge field of the T-bar vector multiplet, respectively.