Boundary Conformal Field Theory and a Boundary Central Charge

TL;DR

This paper explores the relationship between boundary central charges and boundary correlation functions in conformal field theories with boundaries, introducing new conformal blocks, analyzing universality, and presenting an interacting model related to graphene.

Contribution

It establishes a relation between boundary central charge and displacement operator correlation, introduces boundary conformal blocks, and presents a boundary-interacting CFT model with novel properties.

Findings

Boundary central charge relates to displacement operator correlations.

Universal structure of current and stress tensor two-point functions in free theories.

An interacting boundary CFT model analogous to graphene's infrared fixed point.

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.