Conformal defects in AdS host protected displacement and tilt operators that source bulk Goldstone-like modes with wavelength of order the AdS radius.
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Defects in conformal field theory
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We discuss consequences of the breaking of conformal symmetry by a flat or spherical extended operator. We adapt the embedding formalism to the study of correlation functions of symmetric traceless tensors in the presence of the defect. Two-point functions of a bulk and a defect primary are fixed by conformal invariance up to a set of OPE coefficients, and we identify the allowed tensor structures. A correlator of two bulk primaries depends on two cross-ratios, and we study its conformal block decomposition in the case of external scalars. The Casimir equation in the defect channel reduces to a hypergeometric equation, while the bulk channel blocks are recursively determined in the light-cone limit. In the special case of a defect of codimension two, we map the Casimir equation in the bulk channel to the one of a four-point function without defect. Finally, we analyze the contact terms of the stress-tensor with the extended operator, and we deduce constraints on the CFT data. In two dimensions, we relate the displacement operator, which appears among the contact terms, to the reflection coefficient of a conformal interface, and we find unitarity bounds for the latter.
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Different lattice entanglement cuts at a (2+1)d O(3) quantum critical point realize distinct Rényi-defect universality classes, and the "extraordinary" cut undergoes an order-disorder transition as the Rényi index n is varied around n≈3–4.
Monte Carlo reconstruction via interpolating family and flat histograms computes the Z2-twisted thermodynamic Casimir difference in the critical 3D Ising model as 0.327(2).
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.
Replica one-loop RG of Wilson-Fisher theory with surface random field yields a mixed-stable dirty defect fixed point and logarithmic multiplets in the N o0 limit.
Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
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.
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
Multiway AdS junctions dualize to factorized quantum maps on CFT interfaces, with scattering matrix fixed by junction tension and automorphisms from n-1 stringy modes, independent of background state.
Timelike geodesic-integrated Wightman functions in dS are dual to bulk-operator correlators with a linear combination of an OPE block and its Casimir partner.
Derives explicit OPE coefficients for contact and exchange Witten diagrams and closed-form defect-to-bulk crossing kernels for zero- and surface defects in specific dimensions.
Establishes a one-to-one correspondence between states and p-dimensional defects in higher-form Maxwell theories via an extended Kac-Moody algebra generated by conserved charges from mixed anomalies, mapping dressed Wilson-'t Hooft defects to squeezed energy eigenstates.
Analytic bootstrap plus perturbative RG yields universal constraints on conformal data, new boundary fixed points in d=4-ε, and first extraction of boundary data for the tricritical O(N) model in d=3-ε.
Establishes correspondence between flat, thermal, and defect conformal partial waves via shadow formalism, obtaining thermal blocks from flat four-point and defect two-point functions and reducing the Casimir equation diagonally.
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.
The paper introduces a formalism for constructing conformally invariant defects in Neural Network Field Theories, demonstrates it on two toy scalar models, and provides a neural-network reading of a defect OPE expansion in two-point functions.
Stringy modes in 3D gravitational junctions map to factorized H_in to H_out and H_L to H_R quantum maps involving scattering matrices and relative Virasoro automorphisms in the dual CFT.
At large central charge, BCFT von Neumann entropy with deformed boundaries is reproduced by island entropy in an emergent JT gravity setup with transparent boundary conditions set by the deformation.
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.
GoBlocks is a parallel Go package for recursive conformal-block evaluation that speeds moderate-precision bootstrap work and is demonstrated on mixed-correlator 3D Ising optimisation.
One-loop bulk calculations in holographic BCFT with EOW brane yield scalar correlators whose analytic properties are incompatible with boundary conformal symmetry expectations.
In 6D (2,0) theories, defect supersymmetric Rényi entropy contribution is linear in 1/n and equals a constant times (2b - d2); Casimir energy contribution equals -d2 (up to constant) in the chiral algebra limit.
Monodromy defects in Maxwell theory are analyzed via mapping to hyperbolic space, recovering the defect primary spectrum and showing that Wilson/'t Hooft lines terminate on defects, become decomposable, and follow Chern-Simons topological behavior.
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Conformal defects in AdS host protected displacement and tilt operators that source bulk Goldstone-like modes with wavelength of order the AdS radius.
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Different lattice entanglement cuts at a (2+1)d O(3) quantum critical point realize distinct Rényi-defect universality classes, and the "extraordinary" cut undergoes an order-disorder transition as the Rényi index n is varied around n≈3–4.
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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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Replica one-loop RG of Wilson-Fisher theory with surface random field yields a mixed-stable dirty defect fixed point and logarithmic multiplets in the N o0 limit.
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Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
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A Twist on Scattering from Defect Anomalies
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
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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.
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Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
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Decoding multiway gravitational junctions in AdS in terms of holographic quantum maps
Multiway AdS junctions dualize to factorized quantum maps on CFT interfaces, with scattering matrix fixed by junction tension and automorphisms from n-1 stringy modes, independent of background state.
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CFT Dual for Timelike Geodesic in Lorentzian dS
Timelike geodesic-integrated Wightman functions in dS are dual to bulk-operator correlators with a linear combination of an OPE block and its Casimir partner.
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Aspects of Witten Diagrams for Holographic Defects
Derives explicit OPE coefficients for contact and exchange Witten diagrams and closed-form defect-to-bulk crossing kernels for zero- and surface defects in specific dimensions.
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The state/defect correspondence
Establishes a one-to-one correspondence between states and p-dimensional defects in higher-form Maxwell theories via an extended Kac-Moody algebra generated by conserved charges from mixed anomalies, mapping dressed Wilson-'t Hooft defects to squeezed energy eigenstates.
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Analytic Bootstrap for $O(N)$ Boundary Conformal Field Theories with Interacting Boundaries
Analytic bootstrap plus perturbative RG yields universal constraints on conformal data, new boundary fixed points in d=4-ε, and first extraction of boundary data for the tricritical O(N) model in d=3-ε.
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Thermal conformal partial waves from flat-space and defect CFT
Establishes correspondence between flat, thermal, and defect conformal partial waves via shadow formalism, obtaining thermal blocks from flat four-point and defect two-point functions and reducing the Casimir equation diagonally.
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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.
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Conformal Defects in Neural Network Field Theories
The paper introduces a formalism for constructing conformally invariant defects in Neural Network Field Theories, demonstrates it on two toy scalar models, and provides a neural-network reading of a defect OPE expansion in two-point functions.
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Decoding the string in terms of holographic quantum maps
Stringy modes in 3D gravitational junctions map to factorized H_in to H_out and H_L to H_R quantum maps involving scattering matrices and relative Virasoro automorphisms in the dual CFT.
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Large-c BCFT Entanglement Entropy with Deformed Boundaries from Emergent JT Gravity
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Holographic reconstruction for defect CFTs from $\mathrm{AdS}_p \times S^q$ spacetimes
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Efficient Conformal Block Evaluation with GoBlocks
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Boundary conformal field theory, holography and bulk locality
One-loop bulk calculations in holographic BCFT with EOW brane yield scalar correlators whose analytic properties are incompatible with boundary conformal symmetry expectations.
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From Weyl Anomaly to Defect Supersymmetric R\'enyi Entropy and Casimir Energy
In 6D (2,0) theories, defect supersymmetric Rényi entropy contribution is linear in 1/n and equals a constant times (2b - d2); Casimir energy contribution equals -d2 (up to constant) in the chiral algebra limit.
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Monodromy Defects for Electric-Magnetic Duality, Hyperbolic Space, and Lines
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