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

## TL;DR

This paper computes two-loop quantum corrections to the low-energy effective actions in two-dimensional supersymmetric QED models, revealing exact and non-protected potentials and their implications for related sigma-models.

## Contribution

It provides explicit two-loop corrections to the Kahler potential in N=(2,2) SQED and confirms the one-loop exactness of the generalized Kahler potential in N=(4,4) SQED.

## Key findings

- The generalized Kahler potential in N=(4,4) SQED is one-loop exact.
- Two-loop corrections to the Kahler potential in N=(2,2) SQED are explicitly derived.
- The N=(4,4) sigma-model with torsion is confirmed to be described by the one-loop exact potential.

## Abstract

We study two-loop quantum corrections to the low-energy effective actions in N=(2,2) and N=(4,4) SQED in the Coulomb branch. In the latter model, the low-energy effective action is described by a generalized Kahler potential which depends on both chiral and twisted chiral superfields. We demonstrate that this generalized Kahler potential is one-loop exact and corresponds to the N=(4,4) sigma-model with torsion presented by Rocek, Schoutens and Sevrin. In the N=(2,2) SQED, the effective Kahler 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.