Central Charges for BCFTs and Holography

TL;DR

This paper investigates boundary central charges in BCFTs through field theory and holographic methods, revealing their monotonic behavior under RG flows and analyzing the effects of boundary shape on holographic duals.

Contribution

It introduces a holographic construction for arbitrary boundary shapes in BCFTs and explores the behavior of boundary central charges and energy-momentum tensors.

Findings

Boundary central charges in 3D BCFTs are conjectured to decrease under RG flows.

Holographic models for arbitrary boundary shapes are developed, confirming consistency with Weyl anomaly.

Standard Fefferman-Graham expansion may fail for generic BCFT boundary geometries.

Abstract

In this paper, we study the logarithmic terms in the partition functions of CFTs with boundaries (BCFTs). In three dimensions, their coefficients give the boundary central charges, which are conjectured to be monotonically decreasing functions under the RG flows. We present a few supporting evidences from field theory calculations. In two dimensions, we give a holographic construction (AdS/BCFT) for an arbitrary shape of boundary and calculate its logarithmic term as well as boundary energy momentum tensors, confirming its consistency with the Weyl anomaly. Moreover, we give perturbative solutions of gravity duals for the three dimensional BCFTs with any shapes of boundaries. We find that the standard Fefferman-Graham expansion breaks down for generic choices of BCFT boundaries.