Algebroid Yang-Mills Theories

TL;DR

This paper introduces a new class of gauge theories based on Lie and Courant algebroids, revealing that certain deformations of Yang-Mills theories preserve their core properties while enabling novel topological models.

Contribution

It proposes a framework replacing Lie algebras with algebroids for gauge theories and shows how this leads to mild deformations of Yang-Mills theories with moduli parameters.

Findings

New topological gauge theories in arbitrary dimensions

Deformations of Yang-Mills theories with no propagating modes

Symmetry enhancement at critical points

Abstract

A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently many E-Killing vectors leads to an astonishingly mild deformation of ordinary Yang-Mills theories: Additional fields turn out to carry no propagating modes. Instead they serve as moduli parameters gluing together in part different Yang-Mills theories. This leads to a symmetry enhancement at critical points of these fields, as is also typical for String effective field theories.