Defects in 4d SCFTs from supergravity and holographic renormalization

Abstract

Type IIB string theory admits Janus solutions connecting ${\text{AdS}}_5$ vacua. These geometries correspond to interface conformal field theories and are naturally described in five-dimensional supergravity as ${\text{AdS}}_4$ foliations over an interval. In this work, we introduce a novel type of Janus solution in ${\text{AdS}}_5$, featuring ${\text{AdS}}_2\times S^2$ foliations instead of ${\text{AdS}}_4$. We interpret these solutions as the supergravity duals of line defects in four-dimensional SCFTs and we discuss their D-brane engineering. Our primary tool is Romans supergravity in five dimensions, which provides a simple Type IIB truncation over $S^5$. Within this framework, under specific conditions, we construct regular solutions interpolating between ${\text{AdS}}_5$ and ${\text{AdS}}_2\times {\mathbb{R}}^3$. These geometries represent one-parameter deformations of ${\text{AdS}}_5$ vacua and are characterized by a running profile for two-form gauge potentials and a scalar field in the supergravity bulk. Finally, using holographic renormalization, we explicitly compute the on-shell action of the defect and we discuss the one-point functions in the holographic field theory.

46 pages. v2: minor changes, references added, published version