Defects in conformal field theory

Abstract

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.

57 pages, 5 figures, Matches published version

References in corpus (11)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Duality and defects in rational conformal field theory
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Spinning AdS Propagators
• Boundary terms of conformal anomaly
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
• Remarks on the Convergence Properties of the Conformal Block Expansion
• Holographic Gauge Theories in Background Fields and Surface Operators
• Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory
• The classifying algebra for defects

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