Conformal defects and Goldstone bosons in Anti-de Sitter space

TL;DR

This paper proves the existence of a protected displacement operator for conformal defects in AdS space, linking boundary defect properties to bulk Goldstone bosons, with broad applicability to various models.

Contribution

It provides a general proof of the protected displacement operator in AdS defects, extending previous conjectures and connecting boundary operators to bulk Goldstone modes.

Findings

Displacement operator has protected dimension in AdS defects.

Protected operators source modes with Compton wavelength of order AdS radius.

The proof applies to defects in long-range models and various examples.

Abstract

We study local quantum field theories in Anti-de Sitter (AdS) space, with boundary conditions that break some of the bulk isometries. Specifically, we focus on conformal defects and we prove that their spectrum supports a displacement operator of protected dimension, despite the non-local nature of the conformal theory living at the boundary of AdS. If the defect breaks a global symmetry, a tilt operator is also present. The existence of a displacement was conjectured in arXiv:2508.08250 for Wilson loops in Yang-Mills theories in AdS. Our proof is valid in general and applies, in particular, to defects in long-range models, as we discuss in various examples. In the bulk, the modes sourced by the protected operators have Compton wavelength of order of the AdS radius: they constitute the AdS analogue of the Goldstone bosons for the spontaneous breaking of the corresponding symmetries.