Conformal perturbation theory is applied to surface defects in O(N) models in 4-ε dimensions to reproduce known flows and construct new ones, with controlled changes in displacement and tilt normalizations and novel features like vortices on non-simply-connected manifolds.
Conformal defects and Goldstone bosons in Anti-de Sitter space
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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.
fields
hep-th 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Derives holographic one-point functions, stress tensor and Ward identities for defects in AdS5 and AdS6 from AdS2×S2, AdS2×S3 and AdS3×S2 backgrounds in Romans supergravity.
Generalizes flow ODEs for QFT data in AdS3/AdS4, capturing operator merger-annihilation and level repulsion, with efficiency gains from crossing equations and Padé approximants.
citing papers explorer
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Flowing with Displacements and Tilts: Surface Operators in $O(N)$ Models
Conformal perturbation theory is applied to surface defects in O(N) models in 4-ε dimensions to reproduce known flows and construct new ones, with controlled changes in displacement and tilt normalizations and novel features like vortices on non-simply-connected manifolds.
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Holographic reconstruction for defect CFTs from $\mathrm{AdS}_p \times S^q$ spacetimes
Derives holographic one-point functions, stress tensor and Ward identities for defects in AdS5 and AdS6 from AdS2×S2, AdS2×S3 and AdS3×S2 backgrounds in Romans supergravity.
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QFT as a set of ODEs: higher dimensions
Generalizes flow ODEs for QFT data in AdS3/AdS4, capturing operator merger-annihilation and level repulsion, with efficiency gains from crossing equations and Padé approximants.