The basic cohomology of the twisted N=16, D=2 super Maxwell theory

TL;DR

This paper analyzes a two-dimensional Abelian model related to Hodge theory, extending it to a Witten-type topological theory that aligns with twisted N=16, D=2 super Maxwell theory, preserving Hodge structure and non-vanishing BRST Laplacian.

Contribution

It introduces an extension of a Hodge theory model to a Witten-type topological theory matching twisted N=16, D=2 super Maxwell theory, maintaining Hodge structure and non-zero BRST Laplacian.

Findings

The extended model is of Witten type.

The basic cohomology retains Hodge-type structure.

The BRST Laplacian does not vanish on-shell.

Abstract

We consider a recently proposed two-dimensional Abelian model for a Hodge theory, which is neither a Witten type nor a Schwarz type topological theory. It is argued that this model is not a good candidate for a Hodge theory since, on-shell, the BRST Laplacian vanishes. We show, that this model allows for a natural extension such that the resulting topological theory is of Witten type and can be identified with the twisted N=16, D=2 super Maxwell theory. Furthermore, the underlying basic cohomology preserves the Hodge-type structure and, on-shell, the BRST Laplacian does not vanish.