Lagrangian Formulations of Self-dual Gauge Theories in Diverse Dimensions

TL;DR

This paper develops generalized Lagrangian formulations for self-dual gauge theories in various dimensions, extending previous models and demonstrating invariance under modified Lorentz transformations despite non-manifest symmetry.

Contribution

It introduces a new approach to formulating self-dual gauge theories using arbitrary spacetime decompositions, broadening the scope of existing models.

Findings

Lagrangian formulations for self-dual gauge theories in diverse dimensions.

Proof of invariance under modified Lorentz transformations.

Extension of previous models based on spacetime decomposition.

Abstract

In this work, we study Lagrangian formulations for self-dual gauge theories, also known as chiral $n$-form gauge theories, for $n = 2p$ in $D = 4p+2$ dimensional spacetime. Motivated by a recent formulation of M5-branes derived from the BLG model, we generalize the earlier Lagrangian formulation based on a decomposition of spacetime into $(D-1)$ dimensions plus a special dimension, to construct Lagrangian formulations based on a generic decomposition of spacetime into $D'$ and $D" = D - D'$ dimensions. Although the Lorentz symmetry is not manifest, we prove that the action is invariant under modified Lorentz transformations.