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

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 e-print archive: http://lanl.arXiv.org/abs/1110.3752v2 RON DONAGI ET AL.quantum deformation of the classical product on sheaf cohomology groups, that computes nonperturbative corrections to analogues of 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).

Marginal deformations of heterotic G2 sigma models

“…Similar sectors have been found in the (0, 2) setting [36], and been used to compute exact results in the worldsheet theory [37,38]. The fact that we reproduce expected results on heterotic moduli gives further credence to the original topological twist and BRST proposals in [39,40].…”

“…Although our leading order result is already known from these works, our method can likely be extended to make exact worldsheet statements via topological twisting, in analogy the results of [36][37][38] in the (0, 2) setting. Our arguments borrow from the analysis of the superconformal algebra [39] associated to type II compactifications on manifolds of G 2 holonomy.…”

Testing the (0,2) mirror map

“…For instance, techniques to evaluate B and B/2 model correlators in hybrid models [25,26] have been recently developed [24], and these could be employed to gain insights into this larger set of theories. While we expect a dependence on non-diagonal, but linear, E-parameters, nonlinear E-parameters seem not to affect A/2-twisted V model correlators [27][28][29]. However, the situation is more subtle for A/2-twisted M models, where the supersymmetry constraint relates E and J parameters.…”

Supersymmetric localization in GLSMs for supermanifolds

“…(See e.g. [35][36][37] for a discussion of (0, 2) deformations of tangent bundles of products of projective spaces and results in quantum sheaf cohomology.) Then the M 's are given by:…”