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1. A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)

   https://doi.org/10.1007/JHEP04(2024)140  

   Colafranceschi, Eugenia; Marolf, Donald; Wang, Zhencheng (April 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one ignores normalizations, of positive operators. On the CFT side of the correspondence, any two positive operatorsA, Bwill satisfy the trace inequality Tr(AB) ≤ Tr(A)Tr(B). This relation holds on any Hilbert space$$ \mathcal{H} $$ $H$and is deeply associated with the fact that the algebraB($$ \mathcal{H} $$ $H$) of bounded operators on$$ \mathcal{H} $$ $H$is a type I von Neumann factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate below. In particular, we argue that the Euclidean gravitational path integral respects this inequality at all orders in the semi-classical expansion and with arbitrary higher-derivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for Jackiw-Teitelboim gravity and we also motivate it for more general theories. 

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2. Real-time gravitational replicas: low dimensional examples

   https://doi.org/10.1007/JHEP08(2021)171  

   Colin-Ellerin, Sean; Dong, Xi; Marolf, Donald; Rangamani, Mukund; Wang, Zhencheng (August 2021, Journal of High Energy Physics)

   A bstract We continue the study of real-time replica wormholes initiated in [1]. Previously, we had discussed the general principles and had outlined a variational principle for obtaining stationary points of the real-time gravitational path integral. In the current work we present several explicit examples in low-dimensional gravitational theories where the dynamics is amenable to analytic computation. We demonstrate the computation of Rényi entropies in the cases of JT gravity and for holographic two-dimensional CFTs (using the dual gravitational dynamics). In particular, we explain how to obtain the large central charge result for subregions comprising of disjoint intervals directly from the real-time path integral. 

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3. Black hole bulk-cone singularities

   https://doi.org/10.1007/JHEP07(2024)046  

   Dodelson, Matthew; Iossa, Cristoforo; Karlsson, Robin; Lupsasca, Alexandru; Zhiboedov, Alexander (July 2024, Journal of High Energy Physics)

   Lorentzian correlators of local operators exhibit surprising singularities in theories with gravity duals. These are associated with null geodesics in an emergent bulk geometry. We analyze singularities of the thermal response function dual to propagation of waves on the AdS Schwarzschild black hole background. We derive the analytic form of the leading singularity dual to a bulk geodesic that winds around the black hole. Remarkably, it exhibits a boundary group velocity larger than the speed of light, whose dual is the angular velocity of null geodesics at the photon sphere. The strength of the singularity is controlled by the classical Lyapunov exponent associated with the instability of nearly bound photon orbits. In this sense, the bulk-cone singularity can be identified as the universal feature that encodes the ubiquitous black hole photon sphere in a dual holographic CFT. To perform the computation analytically, we express the two-point correlator as an infinite sum over Regge poles, and then evaluate this sum using WKB methods. We also compute the smeared correlator numerically, which in particular allows us to check and support our analytic predictions. We comment on the resolution of black hole bulk-cone singularities by stringy and gravitational effects into black hole bulk-cone “bumps”. We conclude that these bumps are robust, and could serve as a target for simulations of black hole-like geometries in table-top experiments. 

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4. Shock waves, black hole interiors and holographic RG flows

   https://doi.org/10.1007/JHEP07(2024)052  

   Cáceres, Elena; Patra, Ayan K; Pedraza, Juan F (July 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We study holographic renormalization group (RG) flows perturbed by a shock wave in dimensionsd≥ 2. The flows are obtained by deforming a holographic conformal field theory with a relevant operator, altering the interior geometry from AdS-Schwarzschild to a more general Kasner universe near the spacelike singularity. We introduce null matter in the form of a shock wave into this geometry and scrutinize its impact on the near-horizon and interior dynamics of the black hole. Using out-of-time-order correlators, we find that the scrambling time increases as we increase the strength of the deformation, whereas the butterfly velocity displays a non-monotonic behavior. We examine other observables that are more sensitive to the black hole interior, such as the thermala-function and the entanglement velocity. Notably, thea-function experiences a discontinuous jump across the shock wave, signaling an instantaneous loss of degrees of freedom due to the infalling matter. This jump is interpreted as a ‘cosmological time skip’ which arises from an infinitely boosted length contraction. The entanglement velocity exhibits similar dependence to the butterfly velocity as we vary the strength of the deformation. Lastly, we extend our analyses to a model where the interior geometry undergoes an infinite sequence of bouncing Kasner epochs. 

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5. Descendants in celestial CFT and emergent multi-collinear factorization

   https://doi.org/10.1007/JHEP03(2021)030  

   Ebert, Stephen; Sharma, Atul; Wang, Diandian (March 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract Multi-collinear factorization limits provide a window to study how locality and unitarity of scattering amplitudes can emerge dynamically from celestial CFT, the conjectured holographic dual to gauge and gravitational theories in flat space. To this end, we first use asymptotic symmetries to commence a systematic study of conformal and Kac-Moody descendants in the OPE of celestial gluons. Recursive application of these OPEs then equips us with a novel holographic method of computing the multi-collinear limits of gluon amplitudes. We perform this computation for some of the simplest helicity assignments of the collinear particles. The prediction from the OPE matches with Mellin transforms of the expressions in the literature to all orders in conformal descendants. In a similar vein, we conclude by studying multi-collinear limits of graviton amplitudes in the leading approximation of sequential double-collinear limits, again finding a consistency check against the leading order OPE of celestial gravitons. 

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