Toda-like (0,2) mirrors to products of projective spaces

TL;DR

This paper proposes and tests a new class of Toda-like Landau-Ginzburg mirror models for (0,2) theories on products of projective spaces, extending previous work and verifying their validity through correlation function matching.

Contribution

It introduces an ansatz for (0,2) Toda-like mirrors to (0,2) sigma models on product spaces with tangent bundle deformations, and validates it via correlation function comparisons.

Findings

Successful matching of correlation functions confirms the ansatz.

Identification of redundancies in the Landau-Ginzburg models.

Extension of mirror symmetry constructions to more complex spaces.

Abstract

One of the open problems in understanding (0,2) mirror symmetry concerns the construction of Toda-like Landau-Ginzburg mirrors to (0,2) theories on Fano spaces. In this paper, we begin to fill this gap by making an ansatz for (0,2) Toda-like theories mirror to (0,2) supersymmetric nonlinear sigma models on products of projective spaces, with deformations of the tangent bundle, generalizing a special case previously worked out for P1xP1. We check this ansatz by matching correlation functions of the B/2-twisted Toda-like theories to correlation functions of corresponding A/2-twisted nonlinear sigma models, computed primarily using localization techniques. These (0,2) Landau-Ginzburg models admit redundancies, which can lend themselves to multiple distinct-looking representatives of the same physics, which we discuss.