Low--dimensional sisters of Seiberg-Witten effective theory

TL;DR

This paper explores low-dimensional reductions of 4D supersymmetric Yang--Mills theories, deriving effective lagrangians that illuminate mathematical structures and key features like nonrenormalisation theorems.

Contribution

It provides explicit calculations of effective low-energy lagrangians for reduced supersymmetric theories, revealing their mathematical beauty and insights into 4D supersymmetric properties.

Findings

Derived effective lagrangians for D=1,2,3 reductions

Revealed mathematical structures of low-dimensional theories

Enhanced understanding of nonrenormalisation theorems

Abstract

We consider the theories obtained by dimensional reduction to D=1,2,3 of 4D supersymmetric Yang--Mills theories and calculate there the effective low-energy lagrangia describing moduli space dynamics -- the low-dimensional analogs of the Seiberg--Witten effective lagrangian. The effective theories thus obtained are rather beautiful and interesting from mathematical viewpoint. In addition, their study allows one to understand better some essential features of 4D supersymmetric theories, in particular -- the nonrenormalisation theorems.