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We employ holography to investigate Liu-Mezei renormalization group monotones in conformal field theories influenced by massive flavor degrees of freedom. We examine the entanglement entropy of a spherical subregion in three holographic field theories - $\mathcal{N}=1$ Klebanov-Witten theory, $\mathcal{N}=4$ SYM theory, and ABJM theory - with fundamental flavor. The gravity dual of massive unquenched flavor is described by dynamical D-branes, and we solve their backreaction in the smeared approximation. We compute entanglement entropy using the Ryu-Takayanagi formula in these backreacted geometries. Our findings indicate that the Liu-Mezei A- and F-functions decrease monotonically to leading order in the number of flavors across all examples. Additionally, we calculate the leading flavor contribution to entanglement entropy using an alternative probe brane method that does not require knowledge of backreaction in the bulk geometries. These results consistently match with backreacted calculations in all cases, assuming omission of a specific IR boundary term stemming from a total derivative., Comment: 71 pages, 3 figures, 5 appendices, matches the published version

We present a new derivation of gravitational entropy functionals in higher-curvature theories of gravity using corner terms that are needed to ensure well-posedness of the variational principle in the presence of corners. This is accomplished by cutting open a manifold with a conical singularity into a wedge with boundaries intersecting at a corner. Notably, our observation provides a rigorous definition of the action of a conical singularity that does not require regularization. For Einstein gravity, we compute the R\'enyi entropy of gravitational states with either fixed-periodicity or fixed-area boundary conditions. The entropy functional for fixed-area states is equal to the corner term, whose extremization follows from the variation of the Einstein action of the wedge under transverse diffeomorphisms. For general Lovelock gravity the entropy functional of fixed-periodicity states is equal to the Jacobson--Myers (JM) functional, while fixed-area states generalize to fixed-JM-functional states, having a flat spectrum. Extremization of the JM functional is shown to coincide with the variation of the Lovelock action of the wedge. For arbitrary $F$(Riemann) gravity, under special periodic boundary conditions, we recover the Dong--Lewkowycz entropy for fixed-periodicity states. Since the variational problem in the presence of corners is not well-posed, we conjecture the generalization of fixed-area states does not exist for such theories without additional boundary conditions. Thus, our work suggests the existence of entropy functionals is tied to the existence of corner terms which make the Dirichlet variational problem well-posed., Comment: 46 pages + appendices, 3 figures; v2: minor edits, references added, JHEP version

We provide a consistent first principles prescription to compute gravitational R\'enyi entropy using Hayward corner terms. For Euclidean solutions to Einstein gravity, we compute R\'enyi entropy of Hartle--Hawking and fixed--area states by cutting open a manifold containing a conical singularity into a wedge with a corner. The entropy functional for fixed--area states is equal to the corner term itself, having a flat-entanglement spectrum, while extremization of the functional follows from the variation of the corner term under diffeomorphisms. Notably, our method does not require regularization of the conical singularity, and naturally extends to higher-curvature theories of gravity., Comment: 5 pages, 2 figures; v2: References added; v3: minor edits, PRD version

We use holography to study the spectra of boundary conformal field theories (BCFTs). To do so, we consider a 2-dimensional Euclidean BCFT with two circular boundaries that correspond to dynamical end-of-the-world branes in 3-dimensional gravity. Interactions between these branes inform the operator content and the energy spectrum of the dual BCFT. As a proof of concept, we first consider two highly separated branes whose only interaction is taken to be mediated by a scalar field. The holographic computation of the scalar-mediated exchange reproduces a light scalar primary and its global descendants in the closed-string channel of the dual BCFT. We then consider a gravity model with point particles. Here, the interaction of two separated branes corresponds to a heavy operator which lies below the black hole threshold. However, we may also consider branes at finite separation that "merge" non-smoothly. Such brane mergers can be used to describe unitary sub-threshold boundary-condition-changing operators in the open-string spectrum of the BCFT. We also find a new class of sub-threshold Euclidean bra-ket wormhole saddles with a factorization puzzle for closed-string amplitudes., Comment: 56 pages (including appendices) + references, 23 figures; v3: added construction of excited states in open-string channel, version to appear in JHEP

We study codimension-even conical defects that contain a deficit solid angle around each point along the defect. We show that they lead to a delta function contribution to the Lovelock scalar and we compute the contribution by two methods. We then show that these codimension-even defects appear as Euclidean brane solutions in higher dimensional topological AdS gravity which is Lovelock-Chern-Simons gravity without torsion. The theory possesses a holographic Weyl anomaly that is purely of type-A and proportional to the Lovelock scalar. Using the formula for the defect contribution, we prove a holographic duality between codimension-even defect partition functions and codimension-even brane on-shell actions in Euclidean signature. More specifically, we find that the logarithmic divergences match, because the Lovelock-Chern-Simons action localizes on the brane exactly. We demonstrate the duality explicitly for a spherical defect on the boundary which extends as a codimension-even hyperbolic brane into the bulk. For vanishing brane tension, the geometry is a foliation of Euclidean AdS space that provides a one-parameter generalization of AdS-Rindler space., Comment: 29 pages with three appendices

We study how the standard definitions of ADM mass and Brown-York quasi-local energy generalize to pure Lovelock gravity. The quasi-local energy is renormalized using the background subtraction prescription and we consider its limit for large surfaces. We find that the large surface limit vanishes for asymptotically flat fall-off conditions except in Einstein gravity. This problem is avoided by focusing on the variation of the quasi-local energy which correctly approaches the variation of the ADM mass for large surfaces. As a result, we obtain a new simple formula for the ADM mass in pure Lovelock gravity. We apply the formula to spherically symmetric geometries verifying previous calculations in the literature. We also revisit asymptotically AdS geometries., Comment: 24 pages with two appendices; references added, minor changes to abstract and text, updated to JHEP style