$p$-Form Surface Charges on AdS: Renormalization and Conservation

TL;DR

This paper computes and renormalizes surface charges for p-form fields in AdS spacetime, exploring boundary conditions, conservation laws, and duality, revealing a rich structure of charges and fluxes.

Contribution

It introduces a holographic renormalization scheme for p-form surface charges in AdS and analyzes various boundary conditions and their impact on charge conservation.

Findings

Standard boundary conditions yield conserved zero-mode charges.

Leaky boundary conditions admit infinite charges with flux.

Magnetic charges and electric/magnetic duality are discussed.

Abstract

Surface charges of a $p$-form theory on the boundary of an AdS$_{d+1}$ spacetime are computed. Counter-terms on the boundary produce divergent corner-terms which holographically renormalize the symplectic form. Different choices of boundary conditions lead to various expressions for the charges and the associated fluxes. With the usual standard AdS boundary conditions, there are conserved zero-mode charges. Moreover, we explore two leaky boundary conditions which admit an infinite number of charges forming an Abelian algebra and non-vanishing flux. Finally, we discuss magnetic $p$-form charges and electric/magnetic duality.