CFT in AdS and boundary RG flows

Abstract

Using the fact that flat space with a boundary is related by a Weyl transformation to anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group (RG) flows. We test this idea by discussing in detail the case of the large $N$ critical $O(N)$ model in general dimension $d$, as well as its perturbative descriptions in the epsilon-expansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured $F$-theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, in conjunction with crossing symmetry, gives an efficient way to constrain bulk two-point functions and extract anomalous dimensions of boundary operators.

72 pages, 6 figures; v2: minor changes, references added; v3: minor typos corrected; v4: minor changes, typo corrected in eq. 4.57

References in corpus (47)

• Towards a derivation of holographic entanglement entropy
• Holographic Dual of BCFT
• Chern-Simons Theory with Vector Fermion Matter
• Aspects of AdS/BCFT
• The Bootstrap Program for Boundary CFT_d
• Unitarity and the Holographic S-Matrix
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• The S-matrix Bootstrap I: QFT in AdS
• One Loop Tests of Higher Spin AdS/CFT
• Boundary and Interface CFTs from the Conformal Bootstrap
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• Entanglement entropy for the n-sphere
• Central Charges for BCFTs and Holography
• The g-theorem and quantum information theory
• Partition functions and double-trace deformations in AdS/CFT
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Renyi Entropies for Free Field Theories
• Towards a $C$-theorem in defect CFT
• Universal Entanglement and Boundary Geometry in Conformal Field Theory
• On Holographic Defect Entropy
• Anomalous dimensions in CFT with weakly broken higher spin symmetry
• On the Polyakov-Mellin bootstrap
• An Analytic Approach to BCFT${}_d$
• Analytic Bootstrap for Boundary CFT
• Boundary terms of conformal anomaly
• Conformal field theories in anti-de Sitter space
• Corner contributions to holographic entanglement entropy in AdS4/BCFT3
• Quantum ${\varphi }^4$ Theory in AdS${}_4$ and its CFT Dual
• Irreversibility in quantum field theories with boundaries
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• Holographic RG Flow on the Defect and g-Theorem
• Anomalies, entropy and boundaries
• $O(N)$ Models with Boundary Interactions and their Long Range Generalizations
• On Marginal Operators in Boundary Conformal Field Theory
• On boundary correlators in Liouville theory on AdS${}_2$
• Supersymmetric Liouville theory in AdS${}_2$ and AdS/CFT
• Boundary effects in entanglement entropy
• Relating bulk to boundary entanglement
• Quantum Entanglement on Boundaries
• Free energy and boundary anomalies on ${\mathbb{S}}^a\times {\mathbb{H}}^b$ spaces
• Ising Field Theory on a Pseudosphere
• Non-abelian Toda theory on AdS${}_2$ and AdS${}_2$/CFT${}_2^{1/2}$ duality
• Boundary correlators in WZW model on AdS${}_2$
• Boundary Conformal Anomalies on Hyperbolic Spaces and Euclidean Balls
• Why boundary conditions do not generally determine the universality class for boundary critical behavior
• The Conformal Anomaly in bCFT from Momentum Space Perspective
• Effects of Non-Conformal Boundary on Entanglement Entropy

Cited by in corpus (44)

• Renormalization Group Flows on Line Defects
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Gluon Scattering in AdS from CFT
• Localized magnetic field in the $O(N)$ model
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Defect extremal surface as the holographic counterpart of Island formula
• Monodromy Defects from Hyperbolic Space
• Notes on a Surface Defect in the $O(N)$ Model
• Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory
• Fermions in AdS and Gross-Neveu BCFT
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• Aspects of CFTs on Real Projective Space
• A plane defect in the 3d O$(N)$ model
• On Analytic Bootstrap for Interface and Boundary CFT
• Conformal Surface Defects in Maxwell Theory are Trivial
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Free energy and defect $C$-theorem in free scalar theory
• Opacity from Loops in AdS
• Conformal dispersion relations for defects and boundaries
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• RG flows on two-dimensional spherical defects
• Hamiltonian truncation in Anti-de Sitter spacetime
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Free energy and defect $C$-theorem in free fermion
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Interacting conformal scalar in a wedge
• Renormalization group flows in AdS and the bootstrap program
• Exploring Confinement in Anti-de Sitter Space
• Holographic QFTs on AdS${}_d$, wormholes and holographic interfaces
• RG Flows and Stability in Defect Field Theories
• The O(N)-flavoured replica twist defect
• Phases of theories with fermions in AdS
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Defects, Rigid Holography and $C$-theorems
• Spontaneous symmetry breaking in free theories with boundary potentials
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Information metric on the boundary
• Boundary criticality for the Gross-Neveu-Yukawa models
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Boundary conformal field theory, holography and bulk locality
• Partition functions for $U(1)$ vectors and phases of scalar QED in AdS
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Finite-coupling spectrum of O(N) model in AdS