Displacement Operators and Constraints on Boundary Central Charges

TL;DR

This paper derives constraints on boundary central charges in conformal field theories by relating trace anomalies to displacement operator correlations, providing new bounds and conjectures validated in free theories.

Contribution

It introduces a general method to constrain boundary central charges using correlation functions and proposes a new conjecture linking boundary charges to stress tensor correlators.

Findings

Derived bounds on boundary central charges in 3D and 4D CFTs.

Established a relation between boundary charges and displacement operator correlators.

Validated results in several free conformal field theories.

Abstract

Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. We conjecture a relation between the a-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories.