Manifestly Covariant Polynomial M5-brane Lagrangians

TL;DR

This paper introduces polynomial, covariant M5-brane Lagrangians that simplify quantisation and analysis, maintaining key features like gauge symmetries and selfduality, and connect to the PST formalism.

Contribution

It provides a new polynomial and covariant formulation of M5-brane Lagrangians, facilitating theoretical developments and quantisation.

Findings

Polynomial Lagrangians reduce to PST formalism upon integrating auxiliary fields.

Gauge transformations involve a St"uckelberg shift that does not affect dynamics.

The polynomial Lagrangians preserve the selfduality condition.

Abstract

We present polynomial and manifestly covariant M5-brane Lagrangians along with their analyses involving their dynamics, gauge symmetries and their nonlinear selfduality condition. Such Lagrangians can be particularly useful for developments that are otherwise hindered by a non-polynomial structure and singularity of the Lagrangian such as its quantisation. Although on integrating out some of the auxiliary fields these polynomial Lagrangians reduce to the M5-brane Lagrangian given by the Pasti-Sorokin-Tonin (PST) formalism, in the analysis of the polynomial Lagrangians the only remnant of the non-polynomial structure of the PST type Lagrangian appears in the gauge transformation corresponding to an infinitesimal shift of a St\"uckelberg field. This transformation does not affect the dynamics or the on-shell self-duality condition of the polynomial M5-brane Lagrangians.