## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 17, Number 6 (2013), 1255-1301.

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

Ron Donagi, Josh Guffin, Sheldon Katz, and Eric Sharpe

#### 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 $\overline{27}^3$ couplings in heterotic string compactifications. Previous computations have relied on either physics-based gauged linear sigma model (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).

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 17, Number 6 (2013), 1255-1301.

**Dates**

First available in Project Euclid: 21 August 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1408626542

**Mathematical Reviews number (MathSciNet)**

MR3262522

**Zentralblatt MATH identifier**

1306.81217

#### Citation

Donagi, Ron; Guffin, Josh; Katz, Sheldon; Sharpe, Eric. Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties. Adv. Theor. Math. Phys. 17 (2013), no. 6, 1255--1301. https://projecteuclid.org/euclid.atmp/1408626542