Green-Schwarz mechanism and $\alpha'$-deformed Courant brackets

TL;DR

This paper integrates the Green-Schwarz anomaly cancellation mechanism into an $oldsymbol{ ext{alpha'}}$-deformed generalized geometry, revealing a consistent deformation of the Courant bracket and a modified diffeomorphism group, derived from doubled $oldsymbol{ ext{alpha'}}$-geometry.

Contribution

It introduces an $oldsymbol{ ext{alpha'}}$-deformed generalized geometry framework that naturally incorporates Green-Schwarz gauge transformations and provides gauge and T-duality invariant $oldsymbol{ ext{alpha'}}$ corrections.

Findings

Deformation of the Courant bracket consistent with Green-Schwarz mechanism

Modified diffeomorphism group in $oldsymbol{ ext{alpha'}}$-deformed geometry

Construction of gauge and T-duality invariant $oldsymbol{ ext{alpha'}}$ corrections

Abstract

We establish that the unusual two-form gauge transformations needed in the Green-Schwarz anomaly cancellation mechanism fit naturally into an $\alpha'$-deformed generalized geometry. The algebra of gauge transformations is a consistent deformation of the Courant bracket and features a nontrivial modification of the diffeomorphism group. This extension of generalized geometry emerged from a `doubled $\alpha'$-geometry', which provides a construction of exactly gauge and T-duality invariant $\alpha'$ corrections to the effective action.