Superconformal anomalies for string defects in six-dimensional $\mathcal{N} = (1,0)$ SCFTs

TL;DR

This paper investigates the anomalies of two-dimensional BPS defects in six-dimensional (1,0) superconformal field theories using holography, computing various anomalies and correlators, and confirming their consistency with field theory results.

Contribution

It provides the first holographic computation of defect Weyl anomalies and surface operator expectation values in 6d (1,0) SCFTs, linking supergravity and field theory results.

Findings

Agreement between holographic and field theory anomaly calculations.

Holographic computation of defect gravitational anomaly as a subleading correction.

Confirmation of defect sphere free energy and Wilson loop correspondence.

Abstract

We study the anomalies of two-dimensional BPS defects in six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories. Using a holographic description of these defects furnished by probe D4-branes in AdS${}_7$ solutions of ten-dimensional type IIA supergravity, we compute the two independent defect Weyl anomalies from the on-shell action for a spherical defect and defect sphere entanglement entropy. We find agreement between the holographic prediction for the defect A-type anomaly coming from the defect sphere free energy and the leading large $N$ contribution to the defect `t Hooft anomaly found using anomaly inflow. We also find agreement between the holographic computation of the expectation value of a surface operator wrapping a torus and the supersymmetric localization computation for a circular Wilson loop in $\mathcal{N}=1$ super Yang-Mills theory on $S^5$. Lastly, we holographically compute the defect gravitational anomaly from the Wess-Zumino action of the probe D4-brane, which provides a subleading large $N$ correction to the defect A-type anomaly.