A-twisted heterotic Landau–Ginzburg models

Abstract

a b s t r a c tIn this paper, we apply the methods developed in recent work for constructing A-twisted (2, 2) Landau-Ginzburg models to analogous (0, 2) models. In particular, we study (0, 2) Landau-Ginzburg models on topologically non-trivial spaces away from large-radius limits, where one expects to find correlation function contributions akin to (2, 2) curve corrections. Such heterotic theories admit A-and B-model twists, and exhibit a duality that simultaneously exchanges the twists and dualizes the gauge bundle. We explore how this duality operates in heterotic Landau-Ginzburg models, as well as other properties of these theories, using examples which renormalization-group flow to heterotic nonlinear sigma models as checks on our methods.

The Witten equation, mirror symmetry, and quantum singularity theory

“…We conclude by noting that it would be a very interesting problem to explore how to extend our results to a setting like that treated by Guffin and Sharpe in [GS1,GS2]. They have considered twisted Landau-Ginzburg models without coupling to topological gravity, but over more general orbifolds; whereas our model couples to topological gravity, but we work exclusively with orbifold vector bundles.…”

“…We also thank Marc Krawitz for showing us the Berglund-Hübsch mirror construction, Eric Sharpe for explaining to us some aspects of his work in [GS1, GS2], and Alessandro Chiodo for his insights. The second author would also like to thank T. Kimura for helpful discussions and insights, and the Institut Mittag-Leffler, for providing a stimulating environment for research.…”

Recent developments in heterotic compactifications

“…The papers [9,10,11] and others since (e.g. [12,13,14,15,17]) have begun building the details of those proposed (0,2) quantum cohomology computations, and that is what we shall discuss in this section.…”

An introduction to quantum sheaf cohomology

“…Later, [2] found a general physical argument explaining why (0,2) quantum cohomology can exist physically. Since then, there have been a number of followup papers in the physics literature, including [12,13,19,20,21,22,23,24,27,28].…”