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1. Entanglement negativity and replica symmetry breaking in general holographic states

   https://doi.org/10.1007/JHEP01(2025)022  

   Dong, Xi; Kudler-Flam, Jonah; Rath, Pratik (January 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> The entanglement negativity$$ \mathcal{E} $$ $E$(A:B) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$generically break theℤ_2kreplica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumedℤ_2kreplica symmetry and proposed that the negativity was related to the entanglement wedge cross section. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$indeed break theℤ_2kreplica symmetry. Our argument involves an identity relating$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$to thek-th Rényi entropy on subregionAB^∗in the doubled state$$ {\left.|{\rho}_{AB}\right\rangle}_{A{A}^{\ast }{BB}^{\ast }} $$ ${\left(,{\rho }_{\mathrm{AB}}\right)}_{A{A}^{\ast }{\mathrm{BB}}^{\ast }}$, from which we see that theℤ_2kreplica symmetry is broken down toℤ_k. Fork< 1, which includes the case of$$ \mathcal{E} $$ $E$(A:B) atk= 1/2, we use a modified cosmic brane proposal to derive a new holographic prescription for$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$and show that it is given by a new saddle with multiple cosmic branes anchored to subregionsAandBin the original state. Using our prescription, we reproduce known results for the PSSY model and show that our saddle dominates over previously proposed CFT calculations neark= 1. Moreover, we argue that theℤ_2ksymmetric configurations previously proposed are not gravitational saddles, unlike our proposal. Finally, we contrast holographic calculations with those arising from RTNs with non-maximally entangled links, demonstrating that the qualitative form of backreaction in such RTNs is different from that in gravity. 

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2. Quantum Extremal Surfaces and the Holographic Entropy Cone

   https://doi.org/10.1007/JHEP11(2021)177  

   Akers, Chris; Hernández-Cuenca, Sergio; Rath, Pratik (November 2021, Journal of High Energy Physics)

   A bstract Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI. 

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3. Large N algebras and generalized entropy

   https://doi.org/10.1007/JHEP04(2023)009  

   Chandrasekaran, Venkatesa; Penington, Geoff; Witten, Edward (April 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We construct a Type II_∞von Neumann algebra that describes the largeNphysics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative 1/Ncorrections. Using only the extrapolate dictionary, we show that the entropy of semiclassical states on this algebra is holographically dual to the generalized entropy of the black hole bifurcation surface. From a boundary perspective, this constitutes a derivation of a special case of the QES prescription without any use of Euclidean gravity or replicas; from a purely bulk perspective, it is a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy of an explicit algebra in theG →0 limit of Lorentzian effective field theory quantum gravity. In a limit where a black hole is first allowed to equilibrate and then is later potentially re-excited, we show that the generalized second law is a direct consequence of the monotonicity of the entropy of algebras under trace-preserving inclusions. Finally, by considering excitations that are separated by more than a scrambling time we construct a “free product” von Neumann algebra that describes the semiclassical physics of long wormholes supported by shocks. We compute Rényi entropies for this algebra and show that they are equal to a sum over saddles associated to quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles associated to “bulge” quantum extremal surfaces contribute with a negative sign. 

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4. Euclidean wormholes for individual 2d CFTs

   https://doi.org/10.1007/JHEP04(2024)051  

   Chandra, Jeevan (April 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We interpret appropriate families of Euclidean wormhole solutions of AdS₃gravity in individual 2d CFTs as replica wormholes described by branching around the time-symmetric apparent horizons of black holes sourced by the backreaction of heavy point particles. These wormholes help describe a rich formalism to coarse grain pure states in 2d CFTs dual to the black hole geometries because the wormhole amplitudes match with the Renyi entropies of CFT states obtained by decohering the pure states in a specific way. This formalism can be generalised to coarse grain pure states in several copies of the CFT dual to multi-boundary black holes using wormhole solutions with higher genus boundaries using which we illustrate that coarse graining away the interior of multi-boundary black holes sets the mutual information between any two copies of the dual CFT to zero. Furthermore, this formalism of coarse graining pure states can be extended to decohere transition matrices between pure states which helps interpret more general families of wormhole solutions including those with non replica-symmetric boundary conditions in individual CFTs. The pseudo entropy of the decohered transition matrices has interesting holographic interpretation in terms of the area of minimal surfaces on appropriate black hole or wormhole geometries. The wormhole solutions which show up in the coarse graining formalism also compute the Renyi entropies of Hawking radiation after the Page time in a setup which generalizes the West Coast model to 3d gravity. Using this setup, we discuss the evaporation of one-sided black holes sourced by massive point particles and multi-boundary black holes in 3d gravity. 

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5. Non-planar corrections in ABJM theory from quantum M2 branes

   https://doi.org/10.1007/JHEP11(2024)056  

   Giombi, Simone; Kurlyand, Stefan A; Tseytlin, Arkady A (November 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> The quantization of semiclassical strings in AdS spacetimes yields predictions for the strong-coupling behaviour of the scaling dimensions of the corresponding operators in the planar limit of the dual gauge theory. Finding non-planar corrections requires computing string loops (corresponding to torus and higher genus surfaces), which is a challenging task. It turns out that in the case of theU_k(N) ×U_−k(N) ABJM theory there is an alternative approach: one may semiclassically quantize M2 branes in AdS₄×S⁷/ℤ_kwhich are wrapped around the 11d circle of radius 1/k=λ/N. Such M2 branes are the M-theory generalization of the strings in AdS × CP³. In this work, we show that by expanding in large M2 brane tensionT₂~$$ \sqrt{kN} $$ $\sqrt{\mathrm{kN}}$for fixedk, followed by an expansion in largek, we can predict the largeλasymptotics of the non-planar corrections to the dimensions of the dual ABJM operators. As a specific example, we consider the M2 brane configuration that generalizes the long folded string with large spin in AdS₄, and compute the 1-loop correction to its energy. This calculation allows us to determine non-planar corrections to the universal scaling function or cusp anomalous dimension. We extend our analysis to the semiclassical M2 branes that generalize the “short” and “long” circular strings with two equal angular momenta in CP³. The “short” M2 brane corresponds to a dual operator whose dimension at strong coupling scales as ∆ ∼λ^1/4+ …, and we derive the leading non-planar correction to it. 

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