Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling

TL;DR

This paper calculates Weyl anomaly coefficients for holographic defect CFTs at both weak and strong coupling, revealing a negative coefficient in a finite parameter region, a first for interacting unitary dCFTs.

Contribution

It provides the first explicit example of an interacting unitary dCFT with a negative Weyl anomaly coefficient, comparing weak and strong coupling results for defect anomalies.

Findings

The type-A Weyl anomaly coefficient b can be negative in certain parameter regions.

Strong and weak coupling calculations of anomaly coefficients show agreement in specific limits.

First explicit example of an interacting unitary dCFT with negative anomaly coefficient.

Abstract

We determine the type-A Weyl anomaly coefficient $b$, associated with the intrinsic scalar curvature of the defect, for the class of holographically realised co-dimension two defect CFTs (dCFTs) introduced in arXiv: 2506.14505 and arXiv: 2512.14853. At strong coupling, we employ the dual D5-brane solutions in Euclidean signature, where the defect is supported on an $S^2$ submanifold of the Euclidean $AdS_3\times S^1$ boundary. At weak coupling, we use the classical solutions of the ${\cal N}=4$ SYM equations of motion, previously conjectured to describe the defects dual to the D5-brane configurations. Notably, the coefficient $b$ is found to be negative in a finite region of parameter space. To our knowledge, this constitutes the first explicit example of an {\it interacting} unitary dCFT with $b<0$. We also compute the type-B Weyl anomaly coefficients associated with the extrinsic curvature of the defects, first at strong coupling and subsequently at weak coupling. In a certain limit, we find agreement between the weak- and strong-coupling results for both the type-A and type-B anomaly coefficients.