Gauge Theory Dynamics and Kahler Potential for Calabi-Yau Complex Moduli

TL;DR

This paper calculates exact partition functions and correlators in 2D supersymmetric gauge theories to determine the Kahler potential and metric on Calabi-Yau moduli space, providing insights into string compactifications.

Contribution

It introduces a method to compute the exact Kahler potential for Calabi-Yau moduli using supersymmetric gauge theory techniques, linking gauge theory observables to geometric data.

Findings

Exact two-sphere partition functions computed.

Kahler potential and Zamolodchikov metric derived.

Results applicable to Calabi-Yau moduli space analysis.

Abstract

We compute the exact two-sphere partition function and matrix of two-point functions of operators in the chiral ring with their complex conjugates in two-dimensional supersymmetric gauge theories. For gauge theories that flow in the infrared to a Calabi-Yau nonlinear sigma model, these renormalization group invariant observables determine the exact Kahler potential and associated Zamolodchikov metric in the complex structure moduli space of the Calabi-Yau manifold.