Holographic RG-flows and Boundary CFTs

TL;DR

The work develops a holographic framework for interface and boundary CFTs using a Janus-like AdS_d slicing to realize spatially dependent relevant deformations. By solving the coupled scalar–gravity equations numerically, it constructs ICFT and BCFT RG flows in $d=2$ and $d=4$, including a BCFT regime where the bulk becomes singular. It extends holographic entanglement entropy to these AdS_sliced geometries, computing minimal surfaces for strip geometries and extracting boundary entropy in $d=2$ and a regulated finite part in $d=4$, with clear dependence on the deformation strength. The results illuminate how spatially varying couplings induce interfaces and boundaries in strongly coupled CFTs and offer a concrete gravitational realization along with EE diagnostics, suggesting avenues for analytic (BPS) solutions and higher-dimensional resolutions of singular BCFTs.

Abstract

Solutions of $(d+1)$-dimensional gravity coupled to a scalar field are obtained, which holographically realize interface and boundary CFTs. The solution utilizes a Janus-like $\mathrm{AdS}_d$ slicing ansatz and corresponds to a deformation of the CFT by a spatially-dependent coupling of a relevant operator. The BCFT solutions are singular in the bulk, but physical quantities such as the holographic entanglement entropy can be calculated.

Figures (11)

• Figure 1: Plots of $f(\mu)$ and $\phi(\mu)$ in the ICFT (top row) and BCFT (bottom row) cases with $\Delta=1.202$ and $\lambda_4=-4.8$. We have used $d=2$ with potential given by \ref{['hatpot']}. The family of curves in each plot is generated by varying the value of the source $\beta_-$. The ICFT curves correspond to $\beta_- = 0,0.2,0.4,\dots, 1.2$ while the BCFT curves correspond to $\beta_- = 2,2.5,3,3.5,4$.
• Figure 2: Plot of expectation value $\alpha_+$ (red) and source $\beta_+$ (blue) as a function of the source $\beta_-$
• Figure 3: Plots of $f(\mu)$ and $\phi(\mu)$ in the ICFT (top row) and BCFT (bottom row) cases. We have used $d=4$ with GPPZ potential given by \ref{['gppzpot']}. The family of curves in each plot is generated by varying the value of the source $\beta_-$. The ICFT curves correspond to $\beta_- = 0, 0.03, 0.06, \dots, 0.3$ while the BCFT curves correspond to $\beta_- = 1, 1.03, 1.06, \dots, 1.3$.
• Figure 4: Minimal surface $\gamma_A$ used for the calculation of holographic entanglement entropy.
• Figure 5: Minimal surface for calculation of the holographic entanglement entropy in the strip geometry in the case of a flow to a BCFT.