# BRST symmetry of doubled membrane sigma-models

## TL;DR

This paper explores the BRST symmetry in doubled membrane sigma-models, linking gauge invariance and the strong constraint of double field theory through a consistent projection of Courant sigma-models.

## Contribution

It provides a detailed construction of the doubled membrane sigma-model from a large Courant sigma-model using BRST symmetry and gauge invariance principles.

## Key findings

- BRST symmetry leads to the strong constraint of double field theory.
- A consistent projection yields gauge transformations of the doubled membrane sigma-model.
- Gauge invariance ensures the closure of gauge transformations in the model.

## Abstract

Courant sigma-models encode the geometric and non-geometric fluxes of compactified closed string theory as generalized Wess-Zumino terms and exhibit their relation to Courant algebroids. In recent work, we proposed a doubled membrane sigma-model that establishes the corresponding connection to double field theory and its algebroid structure. The strategy is to consider a "large" Courant sigma-model over a doubled target spacetime and identify a suitable projection that leads to a sigma-model for doubled fields. In this note, we provide further details for this construction. Starting from the BRST symmetry of the BV action that satisfies the classical master equation, we consistently project the BRST transformations of the superfields of the "large" Courant sigma-model to obtain the gauge transformations of the doubled membrane sigma-model. We show that demanding gauge invariance and the closure of gauge transformations of the worldvolume theory, leads to a condition that is in direct correspondence to the strong constraint of the target space double field theory.