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Conformal Defects and Goldstone Bosons in Anti–de Sitter Space

Lorenzo Bianchi*

Elia de Sabbata†

Marco Meineri‡

  • *Contact author: lorenzo.bianchi@unito.it
  • †Contact author: eliadesabbata@gmail.com
  • ‡Contact author: marco.meineri@unito.it
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Phys. Rev. Lett. 137, 111601 – Published 8 September, 2026

DOI: https://doi.org/10.1103/853m-z97v

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 nonlocal 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 Gabai et al. [J. High Energy Phys. 06 (2026) 029] 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.

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Phys. Rev. Lett. 137, 111601– Published 8 September, 2026
  • Received 15 May 2026
  • Accepted 16 July 2026
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