Boundary Conformal Field Theory and a Boundary Central Charge

Abstract

We consider the structure of current and stress tensor two-point functions in conformal field theory with a boundary. The main result of this paper is a relation between a boundary central charge and the coefficient of a displacement operator correlation function in the boundary limit. The boundary central charge under consideration is the coefficient of the product of the extrinsic curvature and the Weyl curvature in the conformal anomaly. Along the way, we describe several auxiliary results. Three of the more notable are as follows: (1) we give the bulk and boundary conformal blocks for the current two-point function; (2) we show that the structure of these current and stress tensor two-point functions is essentially universal for all free theories; (3) we introduce a class of interacting conformal field theories with boundary degrees of freedom, where the interactions are confined to the boundary. The most interesting example we consider can be thought of as the infrared fixed point of graphene. This particular interacting conformal model in four dimensions provides a counterexample of a previously conjectured relation between a boundary central charge and a bulk central charge. The model also demonstrates that the boundary central charge can change in response to marginal deformations.

75 pages, 4 figures; v2: references added. v3: comments on anomalous dimension and references added. v4: minor corrections, published version

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• Boundary Holographic Witten Diagrams
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• Flavours and Infra-red Instability in Holography
• More on Boundary Holographic Witten Diagrams
• Non-relativistic Conformal Field Theory in the Presence of Boundary
• Gravity Dual of Networks
• Critical properties of three-dimensional many-flavour QEDs
• Boundary Conformal Field Theory at Large Charge
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation
• Quench Disorder and Scalar Field Theory in the Presence of Boundary
• Boundary critical behavior of the Gross-Neveu-Yukawa model
• Boundary conformal field theory, holography and bulk locality