Twisting gauged non-linear sigma-models

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.

33 pages; v2: small additions, published version

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• Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
• Localizing non-linear $\mathcal{N}=(2,2)$ sigma model on $S^2$
• Open Gauged Sigma Models, Equivariant Branes, and Equivariant Homological Mirror Symmetry