Holographic reconstruction for defect CFTs from $\mathrm{AdS}_p \times S^q$ spacetimes

Abstract

We study defects in superconformal field theories using holography, focusing on the precise derivation of the defect observables from supergravity. We consider $\mathrm{AdS}_p \times S^q$ spacetimes fibered over an interval and coupled to higher-form gauge fields as well as scalar fields. We determine the coordinate system in which the defect geometry admits an asymptotically flat boundary and, in this setup, we systematically apply holographic renormalization to compute the fundamental observables of the defect theory. In particular, we derive the one-point correlators of the bulk fields, the holographic stress tensor, and its Ward identities. We implement explicitly this procedure for line and surface defects in five- and six-dimensional Romans supergravity. The relevant geometries are $\mathrm{AdS}_2\times S^2$, $\mathrm{AdS}_2\times S^3$ and $\mathrm{AdS}_3\times S^2$ backgrounds warped over an interval, preserving four supercharges and asymptotically $\mathrm{AdS}_5$ and $\mathrm{AdS}_6$. In each case, we discuss the implications of our results and compare them with the standard literature on defects in conformal field theory.