Topological twists of supersymmetric algebras of observables

TL;DR

This paper develops a framework using factorization algebras to perform topological twists of supersymmetric field theories, classifying all such twists and homomorphisms in dimensions 1 to 10.

Contribution

It introduces a novel algebraic approach to topological twisting via factorization algebras and classifies all possible twists and homomorphisms across multiple dimensions.

Findings

Constructs algebras over little disks operad from supersymmetric theories.

Classifies topological supercharges in dimensions 1-10.

Provides a systematic method for topological twisting in field theories.

Abstract

We explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras. Namely, given a supersymmetric factorization algebra with a choice of a topological supercharge we construct an algebra over the operad of little disks. We also explain the role of the twisting homomorphism allowing us to construct an algebra over the operad of framed little disks. Finally, we give a complete classification of topological supercharges and twisting homomorphisms in dimensions $1$ through $10$.