On the generalized Komar charge of Kaluza-Klein theories and higher-form symmetries

TL;DR

This paper extends the concept of Komar charges in Kaluza-Klein theories by incorporating higher-form symmetries, resulting in a conserved charge that accounts for monopole contributions and exhibits electric-magnetic duality.

Contribution

It introduces a modified Komar charge that includes higher-form symmetry contributions, ensuring conservation and duality invariance in Kaluza-Klein gravity.

Findings

The generalized charge includes higher-form symmetry contributions.

The modified charge accounts for Kaluza-Klein monopoles.

The resulting charge is conserved and duality invariant.

Abstract

The generalized Komar $(d-2)$-form charge can be modified by the addition of any other on-shell closed (conserved) $(d-2)$-form charge. We show that, with Kaluza--Klein boundary conditions, one has to add a charge related to the higher-form symmetry identified in Ref.~\cite{Gomez-Fayren:2024cpl} to the naive Komar charge of pure 5-dimensional gravity to obtain a conserved charge charge whose integral at spatial infinity gives the mass. The new term also contains the contribution of the Kaluza--Klein monopole charge leading to electric-magnetic duality invariance.