Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry

TL;DR

This paper constructs a geometrical framework for topological BRST symmetries in Yang-Mills theory, leading to a closed off-shell supersymmetric sector and extending to equivariant theories on special manifolds.

Contribution

It provides a geometrical construction of scalar and vector topological BRST operators that generate a maximally supersymmetric Yang-Mills subalgebra, clarifying the structure of supersymmetry in twisted theories.

Findings

Constructed globally well-defined scalar and vector topological BRST operators.

Derived a subalgebra of maximally supersymmetric Yang-Mills theory that is closed off-shell.

Extended the framework to equivariant topological field theories on manifolds with Killing vectors.

Abstract

The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincar\'e supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting "equivariant topological field theory" corresponds to the twist of super Yang-Mills theory on Omega backgrounds.