F-theory and 2d (0,2) Theories

TL;DR

This paper explores the connection between F-theory compactifications on Calabi-Yau five-folds and two-dimensional (0,2) supersymmetric gauge theories, establishing a geometric-physical dictionary and analyzing anomaly cancellation and dualities.

Contribution

It initiates the study of F-theory on Calabi-Yau five-folds leading to 2d (0,2) theories, providing a geometric-physical correspondence and analyzing anomaly and duality structures.

Findings

Established the dictionary between elliptic fibration data and 2d gauge theories.

Analyzed anomaly cancellation, Green-Schwarz terms, and Chern-Simons couplings.

Proposed a correspondence between F-theory data and heterotic GLSMs.

Abstract

F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via different T-branes or gluing data in F-theory.