General Solution Of Linear Vector Supersymmetry

TL;DR

This paper provides a general, simplified solution to the Ward identity for linear vector supersymmetry in topological models, streamlining the analysis of their algebraic structure and finiteness without complex cohomology methods.

Contribution

It introduces a compact, general solution to the Ward identity for linear vector supersymmetry, simplifying the study of topological models and their finiteness proofs.

Findings

Simplified the proof of finiteness for supersymmetric topological models.

Bypassed complex cohomology techniques in quantum extensions.

Applied the solution to Chern-Simons theory as an example.

Abstract

We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example.