Lagrangian of Self-dual Gauge Fields in Various Formulations

TL;DR

This paper reviews various formulations of the Lagrangian for self-dual gauge theories, introduces a new non-covariant Lagrangian based on spacetime decomposition, and demonstrates its Lorentz invariance in six dimensions.

Contribution

It presents a simple rule for constructing non-covariant Lagrangians for self-dual gauge fields and extends this to complex spacetime decompositions.

Findings

New non-covariant Lagrangian with self-duality proven

The Lagrangian maintains 6D Lorentz invariance

Extension to more complex spacetime decompositions possible

Abstract

The Lagrangian of self-dual gauge theory in various formulations are reviewed. From these results we see a simple rule and use it to present some new non-covariant Lagrangian based on the decomposition of spacetime into $D=D_1+D_2+D_3$. Our prescription could be easily extended to more complex decomposition of spacetime and some more examples are presented therefore. The self-dual property of the new Lagrangian is proved in detail. We also show that the new non-covariant actions give field equations with 6d Lorentz invariance.