AdS/BCFT Correspondence for Higher Curvature Gravity: An Example

TL;DR

The paper shows that in AdS/BCFT with higher curvature gravity, specifically New Massive Gravity in three dimensions, boundary and entanglement entropies retain Einstein-like forms once written with an effective Newton constant $G_{eff}$ and an effective cosmological constant, with the central charge $c$ accordingly renormalized. It demonstrates a holographic g-theorem via the null energy condition on the bulk boundary $Q$, and provides multiple derivations (disk amplitude, holographic entanglement entropy, and auxiliary-field reformulation) that all align. The thermal analysis with BTZ and AdS black holes confirms these results extend to finite-temperature BCFT, though new-type black holes pose challenges due to non-conserved Brown–York charges, requiring a separate treatment. Overall, the work suggests higher curvature corrections in AdS/BCFT can be largely encapsulated by central-charge rescaling, and points to future extensions to broader higher-curvature theories and higher dimensions. The findings offer a consistent framework for incorporating higher-derivative gravity into holographic BCFT, with implications for boundary degrees of freedom and RG flows.

Abstract

We consider the effects of higher curvature terms on a holographic dual description of boundary conformal field theory. Specifically, we consider three-dimensional gravity with a specific combination of Ricci tensor square and curvature scalar square, so called, new massive gravity. We show that a boundary entropy and an entanglement entropy are given by similar expression with those of the Einstein gravity case when we introduce an {\it effective} Newton's constant and an {\it effective} cosmological constant. We also show that the holographic g-theorem still holds in this extension, and we give some comments about the central charge dependence of boundary entropy in the holographic construction. In the same way, we consider new type black holes and comment on the boundary profile. Moreover, we reproduce these results through auxiliary field formalism in this specific higher curvature gravity.