Kosmann derivative and momentum maps from a duality covariant framework

TL;DR

This paper develops a covariant formulation of diffeomorphisms in Double Field Theory using a generalized Kosmann derivative expressed via fluxes and momentum maps, enabling duality-covariant conserved charges and insights into black hole thermodynamics.

Contribution

It introduces a flux-based formulation of the generalized Kosmann derivative with a momentum map, providing a covariant realization of diffeomorphisms in doubled geometry.

Findings

A flux-based covariant Kosmann derivative formulation.

Duality-covariant momentum maps in supergravity.

Implications for conserved charges and black hole thermodynamics.

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.