Twisted N=4 SUSY Algebra in Topological Models of Schwarz Type

TL;DR

This paper explores the twisted N=4 supersymmetry in Schwarz type topological models, showing how certain theories can be untwisted to sigma-models and revealing new fermionic symmetries through dimensional reduction.

Contribution

It demonstrates the untwisting of Chern-Simons and BF models and uncovers previously overlooked fermionic scalar symmetries in these topological theories.

Findings

Chern-Simons theory can be untwisted to a sigma-model in the free case.

Dimensional reduction yields a two-dimensional BF-model with similar untwisting.

New fermionic scalar symmetries are identified in the reduced models.

Abstract

We reinvestigate the twisted N=4 supersymmetry present in Schwarz type topological field models. We show that Chern-Simons theory in three dimensions can be untwisted to a kind of sigma-model with reversed statistics only in the free case. By dimensional reduction we define then the two-dimensional BF-model. We establish an analog result concerning the untwisting. As a consequence of the definition through dimensional reduction we find new fermionic scalar symmetries that have been overlooked so far in the literature.