Conformal defects in AdS host protected displacement and tilt operators that source bulk Goldstone-like modes with wavelength of order the AdS radius.
Canonical reference
A Study of Quantum Field Theories in AdS at Finite Coupling
Canonical reference. 80% of citing Pith papers cite this work as background.
13
Pith papers citing it
Background
80% of classified citations
abstract
We study the $O(N)$ and Gross-Neveu models at large $N$ on AdS$_{d+1}$ background. Thanks to the isometries of AdS, the observables in these theories are constrained by the SO$(d,2)$ conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek, and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS $4$-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in $\frac{1}{N}$, and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic $O(N)$ model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS$_2$ evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.
citation-role summary
background 5
citation-polarity summary
fields
hep-th 13roles
background 4representative citing papers
A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
The authors generalize the AdS₂ flow equations for QFT data to AdS₃ and AdS₄, add crossing-based closure and Padé-accelerated sums, and verify them in free theories.
Computes closed-form one-loop anomalous dimensions for all double-trace operators [φφ]_{n,ℓ} in Φ⁴ theory in AdS₃ for arbitrary n, ℓ and Δ_φ > 1.
Crosscap defects are introduced in CFTs via Z2 quotients, with crossing equations derived and CFT data computed in the O(N) model at Gaussian and Wilson-Fisher points showing absent displacement and tilt operators for generic p.
The one-loop diagram in conformally coupled φ⁴ theory in AdS₃ is expressed as an infinite sum of tree-level diagrams, summed via number-theoretic conjectures to give analytic anomalous dimensions for all dual double-trace operators, with new results in t- and u-channels.
Higher-order large-N and epsilon-expansion calculations of boundary free energies, fermion dimensions, and central charge in the Gross-Neveu-Yukawa universality class, with consistency checks between methods.
Exact infrared solutions for surface criticalities in the Gross-Neveu-Yukawa model encode fermionic anomalies in surface dynamics and reveal emergent structures linked to a defect version of the CFT distance conjecture.
Derives universal first-order ODEs governing the RG flow of boundary operator data (scaling dimensions, OPE and BOE coefficients) for 2D QFTs on hyperbolic space.
Conjecture reducing bulk loop discontinuity integrals in black hole Schwinger-Keldysh geometry to exterior real-time finite-temperature loop integrals, checked at one to three loops for low-point functions.
Simple feed-forward neural networks trained on crossing symmetry plus a single anchor value reproduce CFT correlators to percent-level accuracy, and the authors conjecture this works because physical correlators are the smoothest allowed functions.
A uniformly moving charge's field is a static Coulomb field in geodesic-centered coordinates, and in AdS the same construction yields a closed-form field with exact antipodal covariance whose null-fringe limits give flat-space antipodal matching.
Develops a Functorial QFT approach and applies it to analyze the O(N) model in AdS, focusing on crossed-channel diagram contributions to conformal block decomposition in the non-singlet sector.
citing papers explorer
-
Conformal defects and Goldstone bosons in Anti-de Sitter space
Conformal defects in AdS host protected displacement and tilt operators that source bulk Goldstone-like modes with wavelength of order the AdS radius.
-
Kontorovich-Lebedev-Fourier Space for de Sitter Correlators
A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
-
QFT as a set of ODEs: higher dimensions
The authors generalize the AdS₂ flow equations for QFT data to AdS₃ and AdS₄, add crossing-based closure and Padé-accelerated sums, and verify them in free theories.
-
Closing the loop on $\Phi^4$ in AdS$_3$
Computes closed-form one-loop anomalous dimensions for all double-trace operators [φφ]_{n,ℓ} in Φ⁴ theory in AdS₃ for arbitrary n, ℓ and Δ_φ > 1.
-
Crosscap Defects
Crosscap defects are introduced in CFTs via Z2 quotients, with crossing equations derived and CFT data computed in the O(N) model at Gaussian and Wilson-Fisher points showing absent displacement and tilt operators for generic p.
-
The 2-Dimensional Dual of $\phi^4$ in AdS$_3$
The one-loop diagram in conformally coupled φ⁴ theory in AdS₃ is expressed as an infinite sum of tree-level diagrams, summed via number-theoretic conjectures to give analytic anomalous dimensions for all dual double-trace operators, with new results in t- and u-channels.
-
Boundary criticality in the Gross-Neveu-Yukawa model at higher orders
Higher-order large-N and epsilon-expansion calculations of boundary free energies, fermion dimensions, and central charge in the Gross-Neveu-Yukawa universality class, with consistency checks between methods.
-
Extraordinary Surface Criticalities for Interacting Fermions
Exact infrared solutions for surface criticalities in the Gross-Neveu-Yukawa model encode fermionic anomalies in surface dynamics and reveal emergent structures linked to a defect version of the CFT distance conjecture.
-
QFT as a set of ODEs
Derives universal first-order ODEs governing the RG flow of boundary operator data (scaling dimensions, OPE and BOE coefficients) for 2D QFTs on hyperbolic space.
-
Loops Outside a Black Hole
Conjecture reducing bulk loop discontinuity integrals in black hole Schwinger-Keldysh geometry to exterior real-time finite-temperature loop integrals, checked at one to three loops for low-point functions.
-
Neural Spectral Bias and Conformal Correlators I: Introduction and Applications
Simple feed-forward neural networks trained on crossing symmetry plus a single anchor value reproduce CFT correlators to percent-level accuracy, and the authors conjecture this works because physical correlators are the smoothest allowed functions.
-
Li\'enard--Wiechert fields in AdS and flat-space antipodal matching from geodesic-centered Coulombic data
A uniformly moving charge's field is a static Coulomb field in geodesic-centered coordinates, and in AdS the same construction yields a closed-form field with exact antipodal covariance whose null-fringe limits give flat-space antipodal matching.
-
Strongly Coupled Quantum Field Theory in Anti-de Sitter Spacetime
Develops a Functorial QFT approach and applies it to analyze the O(N) model in AdS, focusing on crossed-channel diagram contributions to conformal block decomposition in the non-singlet sector.