Line and surface defects for the free scalar field

Abstract

For a single free scalar field in $d\ge 2$ dimensions, almost all the unitary conformal defects must be `trivial' in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in $d\ge 4$ and co-dimension three defects in $d\ge 5$. As an intermediate result we show that the $n$-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.

arXiv comment41 pages. v3: matches journal version

References in corpus (56)

• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Spinning Conformal Correlators
• Analyticity in Spin in Conformal Theories
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• The Bootstrap Program for Boundary CFT_d
• Conformal Field Theories Near a Boundary in General Dimensions
• Radial Coordinates for Conformal Blocks
• Causality Constraints in Conformal Field Theory
• Bootstrapping the superconformal index with surface defects
• Bootstrapping the 3d Ising twist defect
• Boundary and Interface CFTs from the Conformal Bootstrap
• Boundary Conformal Field Theory and a Boundary Central Charge
• Energy Momentum Tensor in Conformal Field Theories Near a Boundary
• Wall-Crossing in Coupled 2d-4d Systems
• A non-renormalization theorem for conformal anomalies
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Conformal Invariance in the Long-Range Ising Model
• Conformal boundary states for free bosons and fermions
• Long-range critical exponents near the short-range crossover
• Rényi entropy and conformal defects
• Dual Boundary Conditions in 3d SCFT's
• Surface Defects and Chiral Algebras
• Six-Dimensional Tensionless Strings In The Large N Limit
• Universality at large transverse spin in defect CFT
• An E7 Surprise
• The Random-Bond Ising Model in 2.01 and 3 Dimensions
• An Analytic Approach to BCFT${}_d$
• Weyl anomaly for Wilson surfaces
• Analytic Bootstrap for Boundary CFT
• Bootstrapping the long-range Ising model in three dimensions
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Superconformal surfaces in four dimensions
• Spinning operators and defects in conformal field theory
• 3d Abelian Gauge Theories at the Boundary
• Veneziano Amplitude of Vasiliev Theory
• Bootstrapping boundary-localized interactions
• Vortex--Phonon Interaction
• Radial coordinates for defect CFTs
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• $O(N)$ Models with Boundary Interactions and their Long Range Generalizations
• Mirror symmetry and line operators
• Calogero-Sutherland Approach to Defect Blocks
• Conformal manifolds: ODEs from OPEs
• Irrelevant deformations and the holographic Callan-Symanzik equation
• Spinning conformal defects
• Dispersion Relation for CFT Four-Point Functions
• Conformal anomaly of Wilson surface observables - a field theoretical computation
• Surface operators in the 6d $\mathcal{N}=(2,0)$ theory
• Superconformal Models for Graphene and Boundary Central Charges
• Chern-Simons theory from M5-branes and calibrated M2-branes
• Composite operators near the boundary
• Conformal Manifolds with Boundaries or Defects
• On the Weyl anomaly of Wilson surfaces
• Correlators of Mixed Symmetry Operators in Defect CFTs
• Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function

Cited by in corpus (46)

• Gapless topological phases and symmetry-enriched quantum criticality
• Renormalization Group Flows on Line Defects
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Localized magnetic field in the $O(N)$ model
• Spin Impurities, Wilson Lines and Semiclassics
• Bootstrapping line defects with $O(2)$ global symmetry
• Defect $a$-Theorem and $a$-Maximization
• Monodromy Defects from Hyperbolic Space
• Monodromy Defects in Free Field Theories
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Analytic bootstrap for the localized magnetic field
• Phases of Wilson Lines in Conformal Field Theories
• Conformal Surface Defects in Maxwell Theory are Trivial
• Free energy and defect $C$-theorem in free scalar theory
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Two Point Functions in Defect CFTs
• 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
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Conformal Bootstrap near the edge
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Free energy and defect $C$-theorem in free fermion
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Interacting conformal scalar in a wedge
• Analytic and numerical bootstrap for the long-range Ising model
• Defect Conformal Blocks from Appell Functions
• RG Flows and Stability in Defect Field Theories
• Radiation, entanglement and islands from a boundary local quench
• A Sum Rule for Boundary Contributions to the Trace Anomaly
• Analytic bootstrap for magnetic impurities
• Universal Spinning Casimir Equations and Their Solutions
• The O(N)-flavoured replica twist defect
• Conformal boundary conditions for a 4d scalar field
• 1d Ising model with $1/r^{1.99}$ interaction
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Spontaneous symmetry breaking in free theories with boundary potentials
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Holographic dual of defect CFT with corner contributions
• Rényi Entropy with Surface Defects in Six Dimensions
• From Large to Small $\mathcal{N}=(4,4)$ Superconformal Surface Defects in Holographic 6d SCFTs
• Boundary conformal field theory, holography and bulk locality
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Conformal Defects in Neural Network Field Theories