Effective Lagrangians for (0+1) and (1+1) dimensionally reduced versions of D=4 N=2 SYM theory

TL;DR

This paper derives one-loop effective Lagrangians for dimensionally reduced N=2 supersymmetric Yang-Mills theories in (0+1) and (1+1) dimensions, revealing their supersymmetric quantum mechanics and sigma model structures.

Contribution

It provides explicit one-loop effective Lagrangians for reduced N=2 SYM theories in lower dimensions, connecting quantum mechanics and sigma models.

Findings

Effective Lagrangian in (0+1) dimensions describes N=4 supersymmetric quantum mechanics.

In (1+1) dimensions, the Lagrangian is a twisted N=4 supersymmetric sigma model.

Explicit results are obtained for all gauge groups.

Abstract

We consider dimensionally reduced versions of N=2 four- dimensional supersymmetric Yang-Mills theory and determine the one-loop effective Lagrangians associated with the motion over the corresponding moduli spaces. In the (0+1) case, the effective Lagrangian describes an N=4 supersymmetric quantum mechanics of the Diaconescu--Entin type. In (1+1) dimensions, the effective Lagrangian represents a twisted N=4 supesymmetric sigma model due to Gates, Hull, and Rocek. We discuss the genetic relationship between these two models and present the explicit results for all gauge groups.