# The logarithmic gauged linear sigma model

## TL;DR

This paper develops a new framework for studying stable log R-maps in hybrid gauged linear sigma models, constructing virtual cycles and establishing comparison theorems to facilitate higher genus Gromov-Witten invariants computation.

## Contribution

It introduces the concept of log R-maps and constructs a proper moduli stack with multiple virtual cycles, providing new tools for Gromov-Witten theory in hybrid models.

## Key findings

- Construction of a proper moduli stack of stable log R-maps.
- Development of two virtual cycles: canonical and reduced.
- Establishment of comparison theorems linking these virtual cycles.

## Abstract

We introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and reduced) are constructed for these moduli stacks. The main results are two comparison theorems relating the reduced virtual cycle to the cosection localized virtual cycle, as well as the reduced virtual cycle to the canonical virtual cycle. This sets the foundation of a new technique for computing higher genus Gromov-Witten invariants of complete intersections.