Alternative Formulation for Duality-Symmetric Eleven-Dimensional Supergravity Coupled to Super M-5-Brane

TL;DR

This paper introduces a simplified duality-symmetric formulation of eleven-dimensional supergravity with gauge fields, avoiding the need for scalar auxiliary fields and enabling a consistent super M-5-brane coupling.

Contribution

It proposes a new lagrangian with a non-propagating auxiliary tensor, completing the superspace formulation, and presents an alternative super M-5-brane action.

Findings

Simpler lagrangian with auxiliary tensor replaces scalar fields

Achieves duality symmetry without explicit self-duality constraints

Provides a consistent coupling to super M-5-brane

Abstract

We present an alternative formulation of duality-symmetric eleven-dimensional supergravity with both three-form and six-form gauge fields. Instead of the recently-proposed scalar auxiliary field, we use a simpler lagrangian with a non-propagating auxiliary multiplier tensor field with eight-indices. We also complete the superspace formulation in a duality-symmetric manner. An alternative super M-5-brane action coupled to this eleven-dimensional background is also presented. This formulation bypasses the usual obstruction for an invariant lagrangian for a self-dual three-form field strength, by allowing the self-duality only as a solution for field equations, but not as a necessary condition.