Abelian matrix models in two loops

TL;DR

This paper calculates the two-loop effective Lagrangian for a supersymmetric quantum mechanical system derived from 4D N=1 supersymmetric QED, revealing a specific correction to the moduli space metric that vanishes in the N=2 case.

Contribution

It provides the first two-loop correction to the moduli space metric in this class of supersymmetric matrix models, confirming the expected vanishing in the N=2 scenario.

Findings

Two-loop correction to the metric is proportional to 1/A^6.

Correction vanishes for the Abelian 4D, N=2 theory.

Results match theoretical expectations for supersymmetric models.

Abstract

We perform a two-loop calculation of the effective Lagrangian for the low--energy modes of the quantum mechanical system obtained by dimensional reduction from 4D, N = 1 supersymmetric QED. The bosonic part of the Lagrangian describes the motion over moduli space of vector potentials A_i endowed with a nontrivial conformally flat metric. We determined the coefficient of the two-loop correction to the metric, which is proportional to 1/A^6. For the matrix model obtained from Abelian 4D, N = 2 theory, this correction vanishes, as it should.