Holographic Weyl Anomalies for 4d Defects in 6d SCFTs

TL;DR

This paper uses holography to analyze 4d defects in 6d SCFTs, computing Weyl anomaly coefficients and stress-energy contributions, confirming consistency with energy conditions, and resolving a supergravity discrepancy.

Contribution

It provides the first holographic calculations of Weyl anomaly coefficients for 4d defects in 6d SCFTs and verifies their physical consistency.

Findings

Computed defect contributions to entanglement entropy.

Determined two Weyl anomaly coefficients for 4d defects.

Confirmed non-negativity of A-type Weyl anomaly coefficient.

Abstract

In this note, we study $1/4$- and $1/2$-BPS co-dimension two superconformal defects in the $6d$ $\mathcal{N}=(2,0)$ $A_{N-1}$ SCFT at large $N$ using their holographic descriptions as solutions of $11d$ supergravity. In this regime, we are able to compute the defect contribution to the sphere entanglement entropy and the change in the stress-energy tensor one-point function due to the presence of the defect using holography. From these quantities, we are then able to unambiguously compute the values for two of the twenty-nine total Weyl anomaly coefficients that characterize $4d$ conformal defects in six and higher dimensions. We are able to demonstrate the consistency of the supergravity description of the defect theories with the average null energy condition on the field theory side. For each class of defects that we consider, we also show that the A-type Weyl anomaly coefficient is non-negative. Lastly, we uncover and resolve a discrepancy between the on-shell action of the $7d$ $1/4$-BPS domain wall solutions and that of their $11d$ uplift.