Two Point Functions in Defect CFTs

Abstract

This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic $d$-dimensional conformal field theory with a flat $p$-dimensional defect and $d-p=q$ co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ${\mathbb{R}}^p\times ({\mathbb{R}}^q/{\mathbb{Z}}_2)$ and a free four dimensional Maxwell theory on a wedge.

arXiv comment34 pages, supplementary Mathematica notebook available; v2: Revised the discussion of embedding space in the Intro, corrected typos, results unchanged

References in corpus (20)

• Spinning Conformal Correlators
• Conformal Field Theories Near a Boundary in General Dimensions
• Averaged Null Energy Condition from Causality
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• Boundary Conformal Field Theory and a Boundary Central Charge
• Energy Momentum Tensor in Conformal Field Theories Near a Boundary
• Defects in conformal field theory
• Dynamical Chiral Symmetry Breaking on a Brane in Reduced QED
• Conformal correlators of mixed-symmetry tensors
• Line and surface defects for the free scalar field
• From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
• Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultra-relativistic limit of graphene
• Spinning operators and defects in conformal field theory
• Bootstrapping boundary-localized interactions
• Radial coordinates for defect CFTs
• Spinning conformal defects
• Renormalization and conformal invariance of non-local quantum electrodynamics
• Correlators of Mixed Symmetry Operators in Defect CFTs
• Thermal Corrections to Renyi Entropies for Conformal Field Theories

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• Monodromy Defects from Hyperbolic Space
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Analytic bootstrap for the localized magnetic field
• On Analytic Bootstrap for Interface and Boundary CFT
• Conformal Surface Defects in Maxwell Theory are Trivial
• RG flows on two-dimensional spherical defects
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Analytic bootstrap for magnetic impurities
• Method of images in defect conformal field theories
• Polyakov's confinement mechanism for generalized Maxwell theory