Localizing non-linear $\mathcal{N}=(2,2)$ sigma model on $S^2$

Abstract

We present a systematic study of $\mathcal{N}=(2,2)$ supersymmetric non-linear sigma models on $S^2$ with the target being a Kähler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological formulation we use a novel version of 2D self-duality which involves a $U(1)$ action on $S^2$. In addition to the generic model we discuss the theory with target space equivariance corresponding to a supersymmetric sigma model coupled to a non-dynamical supersymmetric background gauge multiplet. We discuss the localization locus and perform a one-loop calculation around the constant maps. We argue that the theory can be reduced to some exotic model over the moduli space of holomorphic disks.

51 pages, refs added

References in corpus (3)

• Sphere Partition Functions and the Zamolodchikov Metric
• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• Twisting gauged non-linear sigma-models

Cited by in corpus (1)

• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$