Bubbling Defect CFT's

TL;DR

This work develops a holographic description of half-BPS domain wall operators in ${\cal N}=4$ SYM via defect CFTs, realized by brane constructions with D3, D5, and NS5 configurations. By combining a probe (Karch–Randall) brane analysis with a full IIB supergravity treatment constrained by $OSp(4|4)$ symmetry, the authors derive a warped $AdS_4\times S^2\times S^2$ Ansatz over a 2D base and a complete set of first-order BPS equations and Bianchi identities. They show the backreaction of the five-branes can be captured by fluxes on non-trivial three-spheres, effectively producing bubbling geometries that generalize the LLM construction to defect configurations, with AdS$_5\times S^5$ emerging as a special case. A bootstrap program is outlined where solutions are encoded in the spinor ratio $\alpha/\beta^*$ and boundary data, setting the stage for a systematic study of domain-wall backreaction, flux quantization, and rank changes across defects. The framework connects defect CFT data to smooth gravitational geometries and provides a path to quantify brane charges and boundary phenomena in holography.

Abstract

We study the gravitational description of conformal half-BPS domain wall operators in N=4 SYM, which are described by defect CFT's. These defect CFT's arise in the low energy limit of a Hanany-Witten like brane setup and are described in a probe brane approximation by a Karch-Randall brane configuration. The gravitational backreaction takes the five-branes in AdS_5xS^5 through a geometric transition and turns them into appropriate fluxes which are supported on non-trivial three-spheres.

Figures (4)

• Figure 1: The brane configuration in flat space.
• Figure 2: Probe branes in $AdS_5\times S^5$
• Figure 3: Probe branes in $AdS_5\times S^5$.
• Figure 4: A possibility for the backreacted geometry.