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arXiv:2211.09148 · Journal of High Energy Physics

Universal behavior of entanglement entropies in interface CFTs from general holographic spacetimes

Andreas Karch, Mianqi Wang

Published Jun 23, 2023• 13 citations
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Abstract

Abstract In previous work universal behavior was conjectured for the behavior of the logarithmic terms in the entanglement entropy of intervals in 1+1 dimensional interface conformal field theories (ICFTs). These putative universal terms were exhibited both in free field theories as well as a large class of holographic models. In this work we demonstrate that this same behavior in fact is realized in any holographic ICFT, significantly strengthening the case for the conjecture.

DOI
10.1007/jhep06(2023)145

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Abstract In previous work universal behavior was conjectured for the behavior of the logarithmic terms in the entanglement entropy of intervals in 1+1 dimensional interface conformal field theories (ICFTs). These putative universal terms were exhibited both in free field theories as well as a large class of holographic models. In this work we demonstrate that this same behavior in fact is realized in any holographic ICFT, significantly strengthening the case for the conjecture.
Abstract We study the entanglement entropy in 1+1 dimensional conformal field theories in the presence of interfaces from a holographic perspective. Compared with the well-known case of boundary conformal field theories, interfaces allow for several interesting new observables. Depending on how the interface is located within the entangling region, the entanglement entropies differ and exhibit surprising new patterns and universal relations. While our analysis is performed within the framework of holography, we expect our results to hold more generally.
We conjecture that the universal logarithmic coefficient for capacity of entanglement ccapc_{\mathrm{cap}}ccap​ is bounded below by the corresponding entropy coefficient ceffc_{\mathrm{eff}}ceff​ at conformal interfaces. We prove the bound in free boson and fermion CFTs and in holographic models with interface branes, and establish it using defect perturbation theory. Numerical calculations at interacting interfaces between the tricritical Ising and Ising CFTs further support the bound. Despite this constraint, capacity provides independent interface data. We construct interfaces with identical entropy and energy transmission coefficients but different capacity coefficients, and show that capacity can even increase as entropy decreases.
Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.
We study the entanglement entropy in 1+1 dimensional conformal field theories in the presence of interfaces from a holographic perspective. Compared with the well-known case of boundary conformal field theories, interfaces allow for several interesting new observables. Depending on how the interface is located within the entangling region, the entanglement entropies differ and exhibit surprising new patterns and universal relations. While our analysis is performed within the framework of holography, we expect our results to hold more generally.
We study entanglement transitions for pairs of disjoint intervals in two-dimensional holographic interface conformal field theories. We consider several holographic models with equal central charges on the two sides of the interface: thin-wall geometries with one and two branes, the Janus solution, and the super-Janus solution. We first discuss the finite interface contribution to the entanglement entropy of a single interval, distinguishing intervals that cross the interface from those that lie entirely on one side. We then use the mutual information to locate the transition between connected and disconnected Ryu--Takayanagi geodesic configurations for two intervals. When the interface lies between the two intervals, increasing the boundary entropy log⁡g\log glogg, which provides a measure of interface strength in the models considered here, generally decreases the critical separation at which the connected configuration ceases to dominate. When both intervals lie on the same side of the interface, the behavior is model dependent: the connected phase persists to larger separations in the Janus and super-Janus models, while the critical separation is unchanged in the thin-wall models. Thus, as diagnosed by the two-interval transition, the interface weakens correlations across the interface while preserving or enhancing correlations between regions on the same side. We also identify a universal ``Silver Blaze'' configuration, in which the interface lies inside one of the intervals and the transition occurs at the same location as in a CFT without an interface, independently of the interface parameters and of the holographic model. This universality follows from a cancellation between crossing and non-crossing interface contributions to the mutual information.
We explore interfaces and junctions joining multiple two-dimensional conformal field theories, with the goal of calculating entanglement entropies in their presence and exploring their holographic duals. In chapter 1 we start with an overview of the three subjects, collecting various well-known results and reviewing some foundational works.In chapter 2 we calculate the holographic entanglement entropy in the presence of a conformal interface for a geometric configuration in which the entangling region lies on one side of the interface. For the supersymmetric Janus solution we find exact agreement between the holographic and conformal field theory calculation of the entanglement entropy.In chapter 3 we calculate the entanglement entropy for topological interfaces in rational conformal field theories for the case where the interface lies at the boundary of the entangling interval and for the case where it is located in the center of the entangling interval. We compare the results to each other and also to the left/right entropy of a related boundary conformal field theory. We also comment on the entanglement entropies for topological interfaces in Liouville theory.In chapter 4 we consider entanglement through permeable junctions of N free boson and free fermion conformal field theories. We constrain the form of the general boundary state and calculate the replicated partition functions with interface operators inserted, from which the entanglement entropy is calculated. We find the functional form of the universal and constant terms to be similar to the N=2 case, depending only of the total transmission of the junction and the unit volume of the zero mode lattice. For N>2 we see a subleading divergent term which does not depend on the parameters of the junction. For N=3 we consider some specific geometries and discuss various limits.In chapter 5 we investigate topological interfaces between three-dimensional Abelian Chern-Simons theories in the context of the AdS_3/CFT_2 correspondence. We show that it is possible to connect the topological interfaces in the bulk Chern-Simons theory to topological interfaces in the dual conformal field theory on the boundary. In addition to the [U(1)]^{2N} Chern-Simons theory on AdS_3, we show that it is possible to find boundary counter terms which lead to the N conserved currents in the dual two-dimensional conformal field theory.