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A bstract We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

A bstract I show that an analog of the crossed product construction that takes type 𝐼𝐼𝐼 1 algebras to type 𝐼𝐼 algebras exists also in the type 𝐼 case. This is particularly natural when the local algebra is a non-trivial direct sum of type 𝐼 factors. Concretely, I rewrite the usual type 𝐼 trace in a different way and renormalise it. This new renormalised trace stays well-defined even when each factor is taken to be type 𝐼𝐼𝐼. I am able to recover both type 𝐼𝐼 ∞ as well as type 𝐼𝐼 1 algebras by imposing different constraints on the central operator in the code. An example of this structure appears in holographic quantum error-correcting codes; the central operator is then the area operator.

A bstract We consider 3-dimensional conformal field theories with U( N ) κ Chern-Simons gauge fields coupled to bosonic and fermionic matter fields transforming in the fundamental representation of the gauge group. In these CFTs, we compute in the ’t Hooft large N limit and to all orders in the ’t Hooft coupling λ = N/κ , the thermal two-point correlation functions of the spin s = 0, s = 1 and s = 2 gauge invariant conformal primary operators. These are the lowest dimension single trace scalar, the U(1) current and the stress tensor operators respectively. Our results furnish additional tests of the conjectured bosonization dualities in these theories at finite temperature.

We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to Nf fermions in the limit of large Nf using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff Δmax. In both the Chern-Simons theory, and in the O(N) model at infinite N, we compute the current spectral functions analytically as a function of Δmax and reproduce previous results in the limit that the truncation Δmax is taken to ∞. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.

A bstract Loop-level scattering amplitudes for massless particles have singularities in regions where tree amplitudes are perfectly smooth. For example, a 2 → 4 gluon scattering process has a singularity in which each incoming gluon splits into a pair of gluons, followed by a pair of 2 → 2 collisions between the gluon pairs. This singularity mimics double parton scattering because it occurs when the transverse momentum of a pair of outgoing gluons vanishes. The singularity is logarithmic at fixed order in perturbation theory. We exploit the duality between scattering amplitudes and polygonal Wilson loops to study six-point amplitudes in this limit to high loop order in planar N = 4 super-Yang-Mills theory. The singular configuration corresponds to the limit in which a hexagonal Wilson loop develops a self-crossing. The singular terms are governed by an evolution equation, in which the hexagon mixes into a pair of boxes; the mixing back is suppressed in the planar (large N c ) limit. Because the kinematic dependence of the box Wilson loops is dictated by (dual) conformal invariance, the complete kinematic dependence of the singular terms for the self-crossing hexagon on the one nonsingular variable is determined to all loop orders. The complete logarithmic dependence on the singular variable can be obtained through nine loops, up to a couple of constants, using a correspondence with the multi-Regge limit. As a byproduct, we obtain a simple formula for the leading logs to all loop orders. We also show that, although the MHV six-gluon amplitude is singular, remarkably, the transcendental functions entering the non-MHV amplitude are finite in the same limit, at least through four loops.

Abstract A new approach to solving random matrix models directly in the large N limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large N loop equations are then used to generate values of higher-pt correlation functions based on this guess. Then one tests whether these higher-pt functions are consistent with positivity requirements, e.g., (tr M 2k ) ≥ 0. If not, the guessed values are systematically ruled out. In this way, one can constrain the correlation functions of random matrices to a tiny subregion which contains (and perhaps converges to) the true solution. This approach is tested on single and multi-matrix models and handily reproduces known solutions. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.

Abstract We study the double-scaling limit of SYK (DS-SYK) model and elucidate the underlying quantum group symmetry. The DS-SYK model is characterized by a parameter q, and in the q → 1 and low-energy limit it goes over to the familiar Schwarzian theory. We relate the chord and transfer-matrix picture to the motion of a “boundary particle” on the Euclidean Poincaré disk, which underlies the single-sided Schwarzian model. AdS 2 carries an action of sl $$ \\mathfrak{sl} $$ (2, ℝ) ≃ su $$ \\mathfrak{su} $$ (1, 1), and we argue that the symmetry of the full DS-SYK model is a certain q-deformation of the latter, namely U q $$ {\\mathcal{U}}_{\\sqrt{q}} $$ ( su $$ \\mathfrak{su} $$ (1, 1)). We do this by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a lattice deformation of AdS 2, which has this U q $$ {\\mathcal{U}}_{\\sqrt{q}} $$ ( su $$ \\mathfrak{su} $$ (1, 1)) algebra as its symmetry. We also exhibit the connection to non-commutative geometry of q-homogeneous spaces, by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a non-commutative deformation of AdS 3. There are families of possibly distinct q-deformed AdS 2 spaces, and we point out which are relevant for the DS-SYK model.

A bstract Recently Leutheusser and Liu [1, 2] identified an emergent algebra of Type III 1 in the operator algebra of N = 4 super Yang-Mills theory for large N . Here we describe some 1/ N corrections to this picture and show that the emergent Type III 1 algebra becomes an algebra of Type II ∞ . The Type II ∞ algebra is the crossed product of the Type III 1 algebra by its modular automorphism group. In the context of the emergent Type II ∞ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.

Abstract We apply our previously developed approach to marginal quartic interactions in multiscalar QFTs, which shows that one-loop RG flows can be described in terms of a commutative algebra, to various models in 4d. We show how the algebra can be used to identify optimal scalings of the couplings for taking large N limits. The algebra identifies these limits without diagrammatic or combinatorial analysis. For several models this approach leads to new limits yet to be explored at higher loop orders. We consider the bifundamental and trifundamental models, as well as a matrix-vector model with an adjoint representation. Among the suggested new limit theories are some which appear to be less complex than general planar limits but more complex than ordinary vector models or melonic models.

A bstract We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function | Z ( β + it )| 2 as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.