Donagi, Ron; Guffin, Josh; Katz, Sheldon; Sharpe, Eric Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties. (English) Zbl 1306.81217 Adv. Theor. Math. Phys. 17, No. 6, 1255-1301 (2013). Summary: 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). Cited in 20 Documents MSC: 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) 81T10 Model quantum field theories 14D15 Formal methods and deformations in algebraic geometry 40A25 Approximation to limiting values (summation of series, etc.) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies × Cite Format Result Cite Review PDF Full Text: DOI arXiv