Kosmann derivative and momentum maps from a duality covariant framework

TL;DR

This work develops a covariant realization of generalized diffeomorphisms in Double Field Theory by expressing the generalized Kosmann derivative entirely in terms of generalized fluxes, augmented by a compensating term that acts as a generalized momentum map. By parameterizing these flux-derived transformations with the heterotic supergravity field content, momentum maps emerge at the supergravity level, providing a duality-covariant interpretation of symmetry generators. The framework enables the construction of conserved currents and Noether charges in doubled geometry with internal symmetries, with direct implications for black hole thermodynamics and its higher-derivative corrections, and remains compatible with α′-corrected extensions via the gBdR mechanism. Overall, the results unify diffeomorphisms and gauge symmetries within a manifestly duality-covariant operator and lay the groundwork for duality-invariant analyses of conserved quantities and higher-derivative dynamics in string-inspired gravity.

Abstract

A covariant implementation of diffeomorphisms in the presence of local symmetries is a nontrivial aspect of gravitational theories. In Double Field Theory, this is achieved through the so-called generalized Kosmann derivative. In this work, we show that the generalized Kosmann derivative admits a natural formulation entirely in terms of generalized fluxes through the inclusion of a compensating term that plays the role of a generalized momentum map, yielding a fully determined and covariant operator that provides a covariant realization of generalized diffeomorphisms. When parameterized in terms of the field content of heterotic supergravity, the resulting symmetry transformations give rise to momentum maps at the supergravity level, offering a duality-covariant interpretation of these objects. This framework provides a natural setting for the construction of conserved currents and Noether charges in doubled geometry with internal symmetries, with direct implications for black hole thermodynamics and its higher-derivative corrections in a duality-covariant setting.