Open Gauged Sigma Models, Equivariant Branes, and Equivariant Homological Mirror Symmetry

TL;DR

This paper explores supersymmetric branes in gauged sigma models with toric targets, their mirror descriptions, and the relation of correlation functions to open Gromov-Witten invariants, highlighting supersymmetry breaking mechanisms.

Contribution

It introduces a detailed analysis of equivariant branes in gauged sigma models and their mirror Landau-Ginzburg descriptions, connecting topological correlators to open Gromov-Witten invariants.

Findings

Equivariant branes have mirror descriptions as gauged Landau-Ginzburg branes.

Correlation functions correspond to open Hamiltonian Gromov-Witten invariants.

Supersymmetry breaking arises from nonperturbative open symplectic vortices.

Abstract

We describe supersymmetric A-branes and B-branes in open N=(2,2) dynamically gauged nonlinear sigma models (GNLSM), placing emphasis on toric manifold target spaces. For a subset of toric manifolds, these equivariant branes have a mirror description as branes in gauged Landau-Ginzburg models with neutral matter. We then study correlation functions in the topological A-twisted version of the GNLSM, and identify their values with open Hamiltonian Gromov-Witten invariants. Supersymmetry breaking can occur in the A-twisted GNLSM due to nonperturbative open symplectic vortices, and we canonically BRST quantize the mirror theory to analyze this phenomenon.