Euclidean D-branes and higher-dimensional gauge theory

TL;DR

The paper establishes that worldvolume theories of euclidean D-branes wrapping manifolds with exceptional holonomy arise as cohomological field theories obtained by dimensionally reducing 10-dimensional SYM to seven and eight dimensions on Spin(7) and G2 manifolds. It provides explicit Lagrangians, field decompositions, and BRST transformations, demonstrating on-shell nilpotency and, in off-shell refinements, a balanced topological field theory structure with dual BRST operators and SL(2) symmetry. The work proves conjectures by BKS and AOS about the topological nature of these higher-dimensional instanton moduli spaces and constructs a related monopole moduli theory in seven dimensions, connected to instanton equations via dimensional reduction. This framework supports a higher-dimensional Floer-type interpretation for calibrated D-branes and offers a robust method to compute topological invariants of moduli spaces in Spin$(7)$ and $G_2$ geometries, with potential implications for calibrated branes and non-perturbative dynamics in string theory.

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.