Topological Matter in Four Dimensions

TL;DR

This paper introduces four-dimensional topological models coupled with matter, derived from twisted supersymmetry and superspace, revealing new features like symmetry breaking mechanisms and mirror symmetry analogs in higher dimensions.

Contribution

It presents novel four-dimensional topological matter models based on twisted supersymmetry and superspace, expanding the understanding of topological quantum field theories.

Findings

Models exhibit new topological features

Potential mechanisms for symmetry breaking

Analog of mirror symmetry in four dimensions

Abstract

Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four dimensions. The framework in which the construction is based is constituted by the superspace associated to these algebras. The models show new features of topological quantum field theories which could provide either a mechanism for topological symmetry breaking, or the analog of two-dimensional mirror symmetry in four dimensions.