Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties

TL;DR

This paper develops simplified mathematical methods to compute quantum sheaf cohomology for deformations of tangent bundles in toric varieties, advancing beyond previous physics-based and brute-force approaches.

Contribution

It introduces new techniques for computing quantum sheaf cohomology, providing more general results and simplifying complex calculations for deformations of tangent bundles.

Findings

Simplified computational methods for quantum sheaf cohomology

More general results than previous GLSM-based computations

Rigorous proofs to be published separately

Abstract

In this paper, we will outline computations of quantum sheaf cohomology for deformations of tangent bundles of toric varieties, for those deformations describable as deformations of toric Euler sequences. Quantum sheaf cohomology is a heterotic analogue of quantum cohomology, a quantum deformation of the classical product on sheaf cohomology groups, that computes nonperturbative corrections to analogues of (27*)^3 couplings in heterotic string computations. Previous computations have relied on either physics-based GLSM techniques or computation-intensive brute-force Cech cohomology techniques. This paper describes methods for greatly simplifying mathematical computations, and derives more general results than previously obtainable with GLSM techniques. We will outline recent results (rigorous proofs will appear elsewhere).