Chern-Simons and Twisted Supersymmetry in Higher Dimensions

TL;DR

This paper explores special supersymmetric gauge theories in higher dimensions, their compactifications, and connections to D-branes and special holonomy manifolds, revealing new structures in supersymmetry and gauge theory.

Contribution

It introduces novel higher-dimensional supersymmetric gauge theories and analyzes their compactifications, linking them to moduli spaces and D-brane configurations.

Findings

Construction of supersymmetric theories in 3, 5, 7, 9 dimensions.

Compactification yields supersymmetric quantum mechanics on moduli spaces.

Discussion of theories with matter and their geometric implications.

Abstract

We describe special supersymmetric gauge theories in three, five, seven and nine dimensions, whose compactification on two-, four-, six- and eight-folds produces a supersymmetric quantum mechanics on moduli spaces of holomorphic bundles and/or solutions to the analogues of instanton equations in higher dimensions. The theories may occur on the worldvolumes of D-branes wrapping manifolds of special holonomy. We also discuss the theories with matter.