Low-energy effective action in two-dimensional SQED: a two-loop analysis

Abstract We study two-loop quantum corrections to the low-energy effective actions in N = 2 2 $$ \mathcal{N}=\left(2,2\right) $$ and N = 4 4 $$ \mathcal{N}=\left(4,4\right) $$ SQED on the Coulomb branch. In the latter model, the low-energy effective action is described by a generalized Kähler potential which depends on both chiral and twisted chiral superfields. We demonstrate that this generalized Kähler potential is one-loop exact and corresponds to the N = 4 4 $$ \mathcal{N}=\left(4,4\right) $$ sigma-model with torsion presented by Roček, Schoutens and Sevrin [1]. In the N = 2 2 $$ \mathcal{N}=\left(2,2\right) $$ SQED, the effective Kähler potential is not protected against higher-loop quantum corrections. The two-loop quantum corrections to this potential and the corresponding sigma-model metric are explicitly found