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1. Near conformal perturbation theory in SYK type models

   https://doi.org/10.1007/JHEP12(2020)171  

   Das, Sumit R.; Ghosh, Animik; Jevicki, Antal; Suzuki, Kenta (December 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbative scheme of arXiv:1608.07567 based on a specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large- N saddle point. While this breaking term formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of O (1) corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large q limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced O ( J ) and the subleading O (1) contributions originate from the Schwarzian dynamics of the soft mode and its interaction with h = 2 (bi-local) matter. 

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2. Real-time gravitational replicas: formalism and a variational principle

   https://doi.org/10.1007/JHEP05(2021)117  

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

   null (Ed.)

   A bstract This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve complex metrics, and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our formulation can be used even in the presence of non-analytic boundary-sources. Furthermore, at least for replica- and CPT-symmetric saddles we show that the metrics may be taken to be real in regions spacelike separated from a so-called ‘splitting surface’. This feature is an important hallmark of unitarity in a field theory dual. 

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3. Eventual Discounting Temporal Logic Counterfactual Experience Replay

   Cameron Voloshin; Abhinav Verma; Yisong Yue (January 2023, arXivorg)

   Linear temporal logic (LTL) offers a simplified way of specifying tasks for policy optimization that may otherwise be difficult to describe with scalar reward functions. However, the standard RL framework can be too myopic to find maximally LTL satisfying policies. This paper makes two contributions. First, we develop a new value-function based proxy, using a technique we call eventual discounting, under which one can find policies that satisfy the LTL specification with highest achievable probability. Second, we develop a new experience replay method for generating off-policy data from on-policy rollouts via counterfactual reasoning on different ways of satisfying the LTL specification. Our experiments, conducted in both discrete and continuous state-action spaces, confirm the effectiveness of our counterfactual experience replay approach. 

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4. Entropy of causal diamond ensembles

   https://doi.org/10.21468/SciPostPhys.15.1.023  

   Jacobson, Ted; Visser, Manus R (July 2023, SciPost Physics)

   We define a canonical ensemble for a gravitational causal diamond by introducing an artificial York boundary inside the diamond with a fixed induced metric and temperature, and evaluate the partition function using a saddle point approximation. For Einstein gravity with zero cosmological constant there is no exact saddle with a horizon, however the portion of the Euclidean diamond enclosed by the boundary arises as an approximate saddle in the high-temperature regime, in which the saddle horizon approaches the boundary. This high-temperature partition function provides a statistical interpretation of the recent calculation of Banks, Draper and Farkas, in which the entropy of causal diamonds is recovered from a boundary term in the on-shell Euclidean action. In contrast, with a positive cosmological constant, as well as in Jackiw-Teitelboim gravity with or without a cosmological constant, an exact saddle exists with a finite boundary temperature, but in these cases the causal diamond is determined by the saddle rather than being selected a priori. 

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5. Semiclassical 3D gravity as an average of large-c CFTs

   https://doi.org/10.1007/JHEP12(2022)069  

   Chandra, Jeevan; Collier, Scott; Hartman, Thomas; Maloney, Alexander (December 2022, Journal of High Energy Physics)

   A bstract A two-dimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large central charge c and a sparse low energy spectrum. This constrains the OPE coefficients and density of states of the CFT via the conformal bootstrap. We define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical 3D gravity. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the ensemble-averaged CFT at large c . The one-loop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger. 

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