Advances in Theoretical and Mathematical Physics

Volume 17 (2013)

Number 6

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

Pages: 1255 – 1301

DOI: http://dx.doi.org/10.4310/ATMP.2013.v17.n6.a2

Authors

Ron Donagi (Department of Mathematics, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Josh Guffin (Department of Mathematics, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Sheldon Katz (Department of Mathematics, University of Illinois, Urbana, Il., U.S.A.)

Eric Sharpe (Physics Department, Virginia Tech, Blacksburg, Va., U.S.A.)

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).

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