On A-twisted moduli stack for curves from Witten's gauged linear sigma models

TL;DR

This paper defines and studies the A-twisted moduli stack for higher genus curves in Witten's gauged linear sigma models, establishing its properties and relation to known moduli spaces, with implications for string theory and mirror symmetry.

Contribution

It introduces a systematic construction of the A-twisted moduli stack for higher genus curves and proves it is an Artin stack, extending previous genus 0 results.

Findings

The A-twisted moduli stack is an Artin stack.

For genus 0, it coincides with known A-twisted moduli space.

The paper connects the moduli stack to stable maps and mirror symmetry.

Abstract

Witten's gauged linear sigma model [Wi1] is one of the universal frameworks or structures that lie behind stringy dualities. Its A-twisted moduli space at genus 0 case has been used in the Mirror Principle [L-L-Y] that relates Gromov-Witten invariants and mirror symmetry computations. In this paper the A-twisted moduli stack for higher genus curves is defined and systematically studied. It is proved that such a moduli stack is an Artin stack. For genus 0, it has the A-twisted moduli space of [M-P] as the coarse moduli space. The detailed proof of the regularity of the collapsing morphism by Jun Li in [L-L-Y: I and II] can be viewed as a natural morphism from the moduli stack of genus 0 stable maps to the A-twisted moduli stack at genus 0. Due to the technical demand of stacks to physicists and the conceptual demand of supersymmetry to mathematicians, a brief introduction of each topic that is most relevant to the main contents of this paper is given in the beginning and the appendix respectively. Themes for further study are listed in the end.