Local B-model Yukawa couplings from A-twisted correlators

TL;DR

This paper uses exact A-twisted correlators from supersymmetric localization to compute local B-model Yukawa couplings in toric Calabi-Yau varieties, clarifying previous ambiguities through twisted mass deformations.

Contribution

It introduces a new procedure to compute B-model Yukawa couplings from A-twisted correlators and resolves classical intersection number ambiguities.

Findings

Validated the method against known mirror symmetry results

Interpreted classical intersection ambiguities as twisted mass degrees of freedom

Provided a detailed computational framework for local B-model Yukawa couplings

Abstract

Using the exact formula for the A-twisted correlation functions of the two dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model, we reconsider the computation of the B-model Yukawa couplings of the local toric Calabi-Yau varieties. Our analysis is based on an exact result that has been evaluated from the supersymmetric localization technique and careful treatment of its application. We provide a detailed description of a procedure to investigate the local B-model Yukawa couplings and also test our prescription by comparing the results with known expressions evaluated from the local mirror symmetry approach. In particular, we find that the ambiguities of classical intersection numbers of a certain class of local toric Calabi-Yau varieties discovered previously can be interpreted as degrees of freedom of the twisted mass deformations.