Dimensional reduction of dual topological theories

TL;DR

This paper explores how certain four-dimensional topological field theories, related to Donaldson and Seiberg-Witten theories, can be systematically reduced to two dimensions, revealing simplified models with preserved topological features.

Contribution

It provides a detailed method for reducing SU(2) Donaldson-Witten and dual Seiberg-Witten theories from four to two dimensions, clarifying their interrelations and topological properties.

Findings

Successful dimensional reduction of Donaldson-Witten theory

Reduction of dual Seiberg-Witten theory to two dimensions

Insights into the topological structure of reduced theories

Abstract

We describe the reduction from four to two dimensions of the SU(2) Donaldson-Witten theory and the dual twisted Seiberg-Witten theory, i.e. the Abelian topological field theory corresponding to the Seiberg--Witten monopole equations.