Twisted N=8, D=2 super Yang-Mills theory as example of a Hodge-type cohomological theory

TL;DR

This paper demonstrates that a specific twisted N=8, D=2 super Yang-Mills theory derived from a higher-dimensional model exemplifies a Hodge-type cohomological structure, linking topological and geometric concepts.

Contribution

It identifies and analyzes the Hodge-type cohomological structure in the twisted N=8, D=2 super Yang-Mills theory through dimensional reduction.

Findings

The theory's generators correspond to de Rham cohomology operators.

A discrete duality operation analogous to the Hodge *-operation is established.

The model provides a concrete example of a Hodge-type cohomological field theory.

Abstract

It is shown that the dimensional reduction of the N_T=2, D=3 Blau-Thompson model to D=2, i.e., the novel topological twist of N=8, D=2 super Yang-Mills theory, provides an example of a Hodge-type cohomological theory. In that theory the generators of the topological shift, co-shift and gauge symmetry, together with a discrete duality operation, are completely analogous to the de Rham cohomology operators and the Hodge *-operation.