Covariant M5-brane action with self-dual 3-form

TL;DR

This paper develops a covariant action for the M5-brane with a self-dual 3-form in eleven-dimensional supergravity, ensuring all symmetries including kappa-symmetry, advancing the theoretical understanding of M5-brane dynamics.

Contribution

It extends previous theories to construct a fully covariant M5-brane action with self-duality and symmetries, including an initial explicit expression attempt.

Findings

Successfully derived a covariant M5-brane action with self-dual 3-form

Ensured the action possesses all necessary symmetries, including kappa-symmetry

Provided an initial explicit form of the action

Abstract

In this work, we extend a theory which describes a linearly self-dual exact 3-form field in six dimensional spacetime within the formalism of arXiv:1511.08220 and arXiv:1903.12196 to an action which fully describes an M5-brane in the eleven-dimensional supergravity background. The action we obtain has all the required symmetries including kappa-symmetry. Although the derivation of the action and the proof the symmetries do not require one to express the action explicitly in terms of the original field contents, we also give an initial attempt to give this expression.