Euclidean super Yang-Mills theory on a hyper-K"ahler manifold

TL;DR

This paper constructs a cohomological gauge theory with N_T=3 on an eight-dimensional hyper-Kähler manifold, expanding the understanding of supersymmetric theories in higher dimensions.

Contribution

It explicitly develops a new cohomological gauge theory on hyper-Kähler eight-folds, building on previous group theoretical descriptions.

Findings

Explicit construction of the N_T=3 cohomological gauge theory.

Extension of gauge theory frameworks to eight-dimensional hyper-Kähler manifolds.

Provides a foundation for further studies in supersymmetric theories in higher dimensions.

Abstract

The construction of a $N_T=3$ cohomological gauge theory on an hyper-K"ahler eight-fold, whose group theoretical descrition was given by Blau and Thompson, is performed explicitly.