BRST symmetry of doubled membrane sigma-models
September 19, 2019
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.
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