M5-brane in the superspace approach

TL;DR

This paper develops a superspace Lagrangian for noninteracting M5-brane tensor multiplets, addressing self-duality constraints and proposing methods for full superspace formulation.

Contribution

It introduces a superspace approach to M5-branes that incorporates self-duality constraints and suggests extensions to achieve a complete superspace description.

Findings

Constructed a superspace Lagrangian for M5-brane tensor multiplets.

Proposed a first-order extension to incorporate self-duality.

Suggested a potential full superspace formulation using integral forms.

Abstract

Motivated by Sen's spacetime prescription for the construction of theories with self-dual field strengths, we present a rigid superspace Lagrangian describing noninteracting tensor multiplets living on a stack of M5-branes and containing all the physical constraints on the fields, yielding the on-shell matching of the degrees of freedom. The geometric superspace approach adopted here offers a natural realization of superdiffeomorphisms and is particularly well suited for the coupling to supergravity. However, within this formulation the (anti-)self-duality property of the 3-form field strengths is lost when the superspace Lagrangian is trivially restricted to spacetime. We propose two main paths to address this issue: a first-order superspace extension of Sen's spacetime results, which, once trivially restricted to spacetime, yields all the dynamical equations including the (anti-)self-duality constraint on the 3-form field strengths, and a possible way to obtain a full superspace description of the theory, based on integral forms.