SymTFT in Superspace

TL;DR

This paper develops a supersymmetric framework for Symmetry Topological Field Theories (SuSymTFT) using supergeometry, extending the bosonic case to fermionic, supersymmetric models.

Contribution

It introduces a super-BF theory formulation of SuSymTFT on supermanifolds, providing a manifestly supersymmetric approach to symmetries and anomalies.

Findings

Constructed the SuSymTFT as a super-BF theory in supermanifolds.

Validated the framework with examples of 2D super-bosons, both compact and chiral.

Extended the symmetry organization to fermionic supersymmetric theories.

Abstract

We propose a manifestly supersymmetric formulation of the Symmetry Topological Field Theory (SuSymTFT) for theories with supersymmetry. The SymTFT is a framework that helps organizing symmetries and anomalies of a QFT. Albeit a lot of activity in the field has been devoted to the construction of the SymTFT for the bosonic symmetry structure, the fermionic case has not been analyzed in detail. Here, we consider the most prominent example of theories exhibiting fermionic symmetries, that is supersymmetric models. These are most naturally formulated on supermanifolds, where the supergeometry approach allows for a manifest organization of the symmetries according to their fermionic grading. We provide the general construction of the SuSymTFT as a super-BF theory living in a (n|m)-dimensional supermanifold and check our proposal in two particular examples, the compact and the chiral super-bosons in two dimensions.