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1. Large p SYK from chord diagrams

   https://doi.org/10.1007/JHEP09(2023)154  

   Mukhametzhanov, Baur (September 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> The p-body SYK model at finite temperature exhibits submaximal chaos and contains stringy-like corrections to the dual JT gravity. It can be solved exactly in two different limits: “large p” SYK 1 ≪p≪Nand “double-scaled” SYKN,p → ∞withλ= 2p²/Nfixed. We clarify the relation between the two. Starting from the exact results in the double-scaled limit, we derive several observables in the large p limit. We compute euclidean 2n-point correlators and out-of-time-order four-point function at long lorentzian times. To compute the correlators we find the relevant asymptototics of the$$ {\mathcal{U}}_q\left( su\left(1,1\right)\right) $$ $U_q\left(\mathrm{su}\left(1,1\right)\right)$6j-symbol. 

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2. Yang-Mills as a Liouville theory

   https://doi.org/10.1016/j.physletb.2023.138229  

   Stieberger, Stephan; Taylor, Tomasz R; Zhu, Bin (November 2023, Physics Letters B)

   We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in two-dimensional Liouville theory tensored with WZW-like chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Tree-level approximation in Yang-Mills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find b^2=(8π^2)^{−1}b_0g^2(M), where b is the Liouville coupling constant, g(M) is the Yang Mills coupling at the renormalization scale M and b_0 is the one-loop coefficient of the Yang-Mills beta function. 

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3. Casimir energy and modularity in higher-dimensional conformal field theories

   https://doi.org/10.1007/JHEP07(2023)028  

   Luo, Conghuan; Wang, Yifan (July 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> An important problem in Quantum Field Theory (QFT) is to understand the structures of observables on spacetime manifolds of nontrivial topology. Such observables arise naturally when studying physical systems at finite temperature and/or finite volume and encode subtle properties of the underlying microscopic theory that are often obscure on the flat spacetime. Locality of the QFT implies that these observables can be constructed from more basic building blocks by cutting-and-gluing along a spatial slice, where a crucial ingredient is the Hilbert space on the spatial manifold. In Conformal Field Theory (CFT), thanks to the operator-state correspondence, we have a non-perturbative understanding of the Hilbert space on a spatial sphere. However it remains a challenge to consider more general spatial manifolds. Here we study CFTs in spacetime dimensionsd >2 on the spatial manifoldT²× ℝ^d−3which is one of the simplest manifolds beyond the spherical topology. We focus on the ground state in this Hilbert space and analyze universal properties of the ground state energy, also commonly known as the Casimir energy, which is a nontrivial function of the complex structure moduliτof the torus. The Casimir energy is subject to constraints from modular invariance on the torus which we spell out using PSL(2,ℤ) spectral theory. Moreover we derive a simple universal formula for the Casimir energy in the thin torus limit using the effective field theory (EFT) from Kaluza-Klein reduction of the CFT, with exponentially small corrections from worldline instantons. We illustrate our formula with explicit examples from well-known CFTs including the criticalO(N) model ind= 3 and holographic CFTs ind ≥3. 

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4. Holographic description of Narain CFTs and their code-based ensembles

   https://doi.org/10.1007/JHEP05(2024)343  

   Aharony, Ofer; Dymarsky, Anatoly; Shapere, Alfred D (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We provide a precise relation between an ensemble of Narain conformal field theories (CFTs) with central chargec=n, and a sum of (U(1) × U(1))ⁿChern-Simons theories on different handlebody topologies. We begin by reviewing the general relation of additive codes to Narain CFTs. Then we describe a holographic duality between any given Narain theory and a pure Chern-Simons theory on a handlebody manifold. We proceed to consider an ensemble of Narain theories, defined in terms of an ensemble of codes of lengthnoverℤ_k × ℤ_kfor primek. We show that averaging over this ensemble is holographically dual to a level-k(U(1) × U(1))ⁿChern-Simons theory, summed over a finite number of inequivalent classes of handlebody topologies. In the limit of largekthe ensemble approaches the ensemble of all Narain theories, and its bulk dual becomes equivalent to “U(1)-gravity” — the sum of the pertubative part of the Chern-Simons wavefunction over all possible handlebodies — providing a bulk microscopic definition for this theory. Finally, we reformulate the sum over handlebodies in terms of Hecke operators, paving the way for generalizations. 

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5. Beyond N = ∞ in large N conformal vector models at finite temperature

   https://doi.org/10.1007/JHEP08(2024)219  

   Diatlyk, Oleksandr; Popov, Fedor K; Wang, Yifan (August 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We investigate finite-temperature observables in three-dimensional largeNcritical vector models taking into account the effects suppressed by$$ \frac{1}{N} $$ $\frac{1}{N}$. Such subleading contributions are captured by the fluctuations of the Hubbard-Stratonovich auxiliary field which need to be handled with care due to a subtle divergence structure which we clarify. The examples we consider include the scalarO(N) model, the Gross-Neveu model, the Nambu-Jona-Lasinio model and the massless Chern-Simons Quantum Electrodynamics. We present explicit results for the free energy density to the subleading order in$$ \frac{1}{N} $$ $\frac{1}{N}$, which captures the thermal one-point function of the stress-energy tensor to this order. We also include the dependence on a chemical potential. We determine the Wilson coefficient in the thermal effective action that is sensitive to global symmetry for the first time directly in interacting CFTs, which produces a symmetry-resolved asymptotic density of states. We further provide a formula from diagrammatics for the one-point functions of general single-trace higher-spin currents. We observe that in most cases considered, these subleading effects lift the apparent degeneracies between observables in different models at infiniteN, while in special cases the discrepancies only start to appear at the next-to-subleading order. 

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