Euclidean D-branes and higher-dimensional gauge theory

TL;DR

This paper explores euclidean D-branes on manifolds with exceptional holonomy, deriving cohomological theories that describe instanton and monopole moduli spaces in higher dimensions, linking string theory with topological gauge theories.

Contribution

It introduces new cohomological field theories from D-branes on special holonomy manifolds, connecting string theory to higher-dimensional gauge theory and topology.

Findings

Constructed a 7D cohomological theory of instantons with Chern-Simons type

Developed a related theory for monopole moduli space on G_2 holonomy manifolds

Linked D-brane configurations to topological invariants of moduli spaces

Abstract

We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane---that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory---is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N_T = 2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G_2 holonomy.