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.