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1. 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)

   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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2. Quantum stabilizer codes, lattices, and CFTs

   https://doi.org/10.1007/JHEP03(2021)160  

   Dymarsky, Anatoly ; Shapere, Alfred ( March 2021 , Journal of High Energy Physics)

   null (Ed.)

   A bstract There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs. More specifically, real self-dual stabilizer codes can be associated with even self-dual Lorentzian lattices, and thus define Narain CFTs. We dub the resulting theories code CFTs and study their properties. T-duality transformations of a code CFT, at the level of the underlying code, reduce to code equivalences. By means of such equivalences, any stabilizer code can be reduced to a graph code. We can therefore represent code CFTs by graphs. We study code CFTs with small central charge c = n ≤ 12, and find many interesting examples. Among them is a non-chiral E 8 theory, which is based on the root lattice of E 8 understood as an even self-dual Lorentzian lattice. By analyzing all graphs with n ≤ 8 nodes we find many pairs and triples of physically distinct isospectral theories. We also construct numerous modular invariant functions satisfying all the basic properties expected of the CFT partition function, yet which are not partition functions of any known CFTs. We consider the ensemble average over all code theories, calculate the corresponding partition function, and discuss its possible holographic interpretation. The paper is written in a self-contained manner, and includes an extensive pedagogical introduction and many explicit examples. 

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3. Spectrum of large N glueballs: holography vs lattice

   https://doi.org/10.1007/JHEP11(2022)164  

   Dymarsky, Anatoly ; Melnikov, Dmitry ( November 2022 , Journal of High Energy Physics)

   Recently there has been a notable progress in the study of glueball states in lattice gauge theories, in particular extrapolating their spectrum to the limit of large number of colorsN. In this note we compare the largeNlattice results with the holographic predictions, focusing on the Klebanov-Strassler model, which describes a gauge theory with$$ \mathcal{N} $$$N$= 1 supersymmetry. We note that glueball spectrum demonstrates approximate universality across a range of gauge theory models. Because of this universality the holographic models can give reliable predictions for the spectrum of pure SU(N) Yang-Mills theories with and without supersymmetry. This is especially important for the supersymmetric theories, for which no firm lattice predictions exist yet, and the holographic models remain the most tractable approach. For SU(N) theories with largeNthe lattice non-supersymmetric and holographic supersymmetric predictions for the mass ratios of the lightest states in various sectors agree up to 5–8%, supporting the proposed universality. In particular, both lattice and holography give predictions for the 2⁺⁺and 1⁻⁻mass ratio, consistent with the known constraints on the pomeron and odderon Regge trajectories.

    

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4. More on torus wormholes in 3d gravity

   https://doi.org/10.1007/JHEP11(2023)039  

   Yan, Cynthia ( November 2023 , Journal of High Energy Physics)

   We study further the duality between semiclassical AdS₃and formal CFT₂ensembles. First, we study torus wormholes (Maldacena-Maoz wormholes with two torus boundaries) with one insertion or two insertions on each boundary and find that they give non-decaying contribution to the product of two torus one-point or two-point functions at late-time. Second, we study the ℤ₂quotients of a torus wormhole such that the outcome has one boundary. We identify quotients that give non-decaying contributions to the torus two-point function at late-time.

   We comment on reflection (R) or time-reversal (T) symmetry vs. the combination RT that is a symmetry of any relativistic field theory. RT symmetry itself implies that to the extent that a relativistic quantum field theory exhibits random matrix statistics it should be of the GOE type for bosonic states and of the GSE type for fermionic states. We discuss related implications of these symmetries for wormholes.

    

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5. Black hole to cosmic horizon microstates in string/M theory: timelike boundaries and internal averaging

   https://doi.org/10.1007/JHEP05(2023)160  

   Silverstein, Eva ( May 2023 , Journal of High Energy Physics)

   In this note, we resolve an apparent obstacle to string/M theory realizations of dS observer patch holography, finding a new role for averaging in quantum gravity. The solvable$$ T\overline{T} $$$T\overline{T}$(+Λ₂) deformation recently provided a detailed microstate count of thedS₃cosmic horizon, reproducing the refined Gibbons-Hawking entropy computed by Anninos et al. along with the correct radial bulk geometry. On the gravity side, the deformation brings in the boundary to just outside a black hole horizon, where it is indistinguishable from the dS cosmic horizon, enabling a continuous passage to a bounded patch of dS. In string/M theory, the relationship between AdS/CFT and dS involves uplifts that change the internal topology, e.g. replacing an internal sphere$$ \mathbbm{S} $$$S$with an internal hyperbolic spaceℍ(and incorporating varying warp and conformal factors). We connect these two approaches, noting that the differences in the extra dimensions between AdS black hole and dS solutions are washed out by internal averaging in the presence of a timelike boundary skirting the horizon. This helps to motivate a detailed investigation into the possibility of such timelike boundaries in (A)dS solutions of string/M theory, and we take initial steps toward suitable generalizations of Liouville walls as one approach.

    

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