Twisting gauged non-linear sigma-models

TL;DR

This paper studies twisted gauged sigma-models with N=2 supersymmetry, showing how they localize to vortex moduli spaces or Kaehler quotients, and connects them to Hamiltonian Gromov-Witten invariants.

Contribution

It introduces a framework for twisting gauged sigma-models into A- and B-models, linking supersymmetric theories to geometric invariants and moduli spaces.

Findings

Gauged A-model localizes to vortex moduli space.

Gauged B-model localizes to Kaehler quotient X//G.

Connects supersymmetric theories to Hamiltonian Gromov-Witten invariants.

Abstract

We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of the vortex equations and computes the Hamiltonian Gromov-Witten invariants. When the target is equivariantly Calabi-Yau, i.e. when its first G-equivariant Chern class vanishes, the supersymmetric theory can also be twisted into a gauged B-model. This model localizes to the Kaehler quotient X//G.