Global aspects of (0,2) moduli space: toric varieties and tangent bundles

TL;DR

This paper investigates the moduli space of (0,2) supersymmetric theories on NEF Fano toric varieties, focusing on tangent bundle deformations, vacuum structures, and conditions for stable compactifications.

Contribution

It characterizes the moduli space as a stack, analyzes vacuum structures, and demonstrates conditions for compactifying the moduli space of smooth A/2 theories.

Findings

Identification of loci with supersymmetry breaking

Description of the moduli space as a stack

Conditions for stable compactifications

Abstract

We study the moduli space of A/2 half-twisted gauged linear sigma models for NEF Fano toric varieties. Focusing on toric deformations of the tangent bundle, we describe the vacuum structure of many (0,2) theories, in particular identifying loci in parameter space with spontaneous supersymmetry breaking or divergent ground ring correlators. We find that the parameter space of such an A/2 theory and its ground ring is in general a moduli stack, and we show in examples that with suitable stability conditions it is possible to obtain a simple compactification of the moduli space of smooth A/2 theories.