Dressing and Screening in Anti-de Sitter

TL;DR

This paper explores gauge-invariant observables in AdS scalar electrodynamics, revealing a novel Higgs mechanism, constructing dressed operators, and analyzing higher-form symmetries relevant for cosmology and de Sitter physics.

Contribution

It introduces a new Higgs mechanism in AdS without a classical VEV, constructs gauge-invariant dressed operators, and analyzes higher-form symmetries and their physical implications.

Findings

Explicit one-loop mass calculation for gauge fields in AdS

Construction of gauge-invariant dressed charged operators

Decoupling of boundary field strengths and higher-form symmetry insights

Abstract

Motivated by a question of defining gauge-invariant observables in cosmology and by the close connection between perturbation theory in de Sitter (dS) and Anti-de Sitter (AdS), we study scalar electrodynamics in AdS in setups that are largely unexplored but relevant for dS physics. For photons with standard (Dirichlet) boundary conditions, we analyze charged scalars whose boundary conditions break the $U(1)$ symmetry. This leads to a nonstandard Higgs mechanism in which the gauge field acquires a one-loop mass without a classical vacuum expectation value. Using recent advances in perturbation theory in AdS, we compute this mass explicitly and evaluate charged-scalar four-point functions. We also provide an alternative derivation based on boundary Ward identities. For photons with alternate (Neumann) boundary conditions, where local charged operators are not gauge invariant, we construct physical observables by dressing charged fields with geodesic Wilson lines. These dressed operators have well-behaved conformal properties and unphysical photon modes decouple from their correlation functions. Explicit one-loop computations further reveal the decoupling of boundary field strengths, for which we provide a nonperturbative argument based on higher-form symmetry. Along the way, we explain the physical consequences of spontaneous breaking of higher-form symmetry in AdS, including the role of the tilt operator, the relation between one-form symmetry and endpoints of Wilson lines at the boundary, and a generalized-symmetry interpretation of conserved currents dual to bulk gauge fields.