Twists and Gorms and Antifields, oh my!

TL;DR

This paper develops a systematic approach to topological twists of supersymmetric theories with open supercharge algebras using BV formalism, and explores their localization, equivariant cohomology, and examples like the equivariant B-model.

Contribution

It introduces an algorithmic construction of twisted theories from supersymmetry data and generalizes to theories with multiple topological supercharges using differential gorms.

Findings

Constructed twisted theories via BV formalism from supersymmetry data.

Explained supersymmetric localization in terms of anticanonical transformations.

Presented examples including a U(1)-equivariant topological B-model.

Abstract

I define topological twists of supersymmetric field theories in the case when the supercharges involved obey an ``open'' algebra. Using the Batalin-Vilkovisky field-antifield formalism, I construct twisted theories algorithmically from the supersymmetry data, and explain supersymmetric localisation in terms of anticanonical transformations. I also treat equivariant topological twists and explain how BV observables contain the equivariant cohomology of the space of histories. Some results are generalised to theories with two topological supercharges -- such as the ``balanced'' topological field theories of Dijkgraaf and Moore -- using the geometry of ``differential gorms'' of Kochan and \v{S}evera. Finally, I exhibit examples of these constructions, including a $\mathrm{U}(1)$-equivariant topological B-model.