Work

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

Year: 2022

Type: article

Abstract: We present a systematic study of $${{\mathcal {N}}}=(2,2)$$ N = ( 2 , 2 ) supersymmetric non-linear sigma models on $$S^2$$ 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 $$S^2$$ 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.

Source: The European Physical Journal C

DOI: 10.1140/epjc/s10052-022-10610-8

Authors: Victor Alekseev, Guido Festuccia, Victor Mishnyakov, Nicolai Terziev, Maxim Zabzine