We suggest and motivate a precise equivalence between uncompactified 11-dimensional $M$ theory the $N=\ensuremath{\infty}$ limit of supersymmetric matrix quantum mechanics describing $D0$ branes. The evidence for conjecture consists several correspondences two theories. As consequence supersymmetry simple model is rich enough to describe properties entire Fock space massless well separated particles supergravity theory. In one particular kinematic situation leading large distance interaction...

We conjecture a sharp bound on the rate of growth chaos in thermal quantum systems with large number degrees freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to commutator operators separated time. that influence this correlator develop no faster than exponentially, Lyapunov exponent $\lambda_L \le 2 \pi k_B T/\hbar$. give precise mathematical argument, based plausible physical assumptions, establishing conjecture.

We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding small number of quanta one side. If these are released scrambling time the past, they destroy local two-sided correlations present unperturbed state. The corresponding bulk geometry is AdS black hole, and key effect blueshift early infalling relative t = 0 slice, creating shock wave. comment string- Planck-scale...

Conformal invariance and unitarity severely limit the possible values of critical exponents in two-dimensional systems.Received 31 January 1984DOI:https://doi.org/10.1103/PhysRevLett.52.1575©1984 American Physical Society

We study the phase diagram of lattice gauge theories coupled to fixed-length scalar (Higgs) fields. consider several groups: ${Z}_{2}$, U(1), and $\mathrm{SU}(N)$. find that when Higgs fields transform like fundamental representation group confining phases are smoothly connected, i.e., they not separated by a boundary. When some other than fundamental, boundary may exist. This is case for $\mathrm{SU}(N)$ with all in adjoint U(1) charge-$N(N>1)$ representation. present an argument due Wegner...

Motivated by the vast string landscape, we consider shear viscosity to entropy density ratio in conformal field theories dual Einstein gravity with curvature square corrections. After redefinitions these reduce Gauss-Bonnet gravity, which has special properties that allow us compute nonperturbatively coupling. By tuning of coupling, value can be adjusted any positive from infinity down zero, thus violating conjectured bound. At linear order also check consistency four different methods...

A bstract Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations entanglement entropy. We show these can be justified using replica trick, geometries with a spacetime wormhole connecting different replicas. In simple model, we study transition in detail by summing topologies. compute related quantities less more complicated models, including JT gravity coupled conformal matter and SYK model. Separately, give direct gravitational argument...

In [1] we gave a precise holographic calculation of chaos at the scrambling time scale. We studied influence small perturbation, long in past, on two-sided correlation function thermofield double state. A similar analysis applies to squared commutators and other out-of-time-order one-sided correlators [2-6]. The essential bulk physics is high energy scattering problem near horizon an AdS black hole. above papers used Einstein gravity study this problem; present paper consider stringy...

In recent work we showed that, for a class of conformal field theories (CFT) with Gauss-Bonnet gravity dual, the shear viscosity to entropy density ratio, eta/s, could violate conjectured Kovtun-Starinets-Son bound, eta/s > or = 1/4 pi. this Letter argue, in context same model, that tuning below (16/25)(1/4 pi) induces microcausality violation CFT, rendering theory inconsistent. This is concrete example which inconsistency and lower bound on are correlated, supporting idea possible universal...

A bstract We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by random matrix dynamics characteristic quantum chaotic systems. Our main tool Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model hole. an analytically continued partition function | Z ( β + it )| 2 well correlation functions diagnostics. Using numerical techniques establish at times. determine early exactly double scaling limit, giving us plausible...

Using gauge/gravity duality, we explore a class of states two CFTs with large degree entanglement, but very weak local two-sided correlation. These are constructed by perturbing the thermofield double state thermal-scale operators that at different times. Acting on dual black hole geometry, these perturbations create an intersecting network shock waves, supporting long wormhole. Chaotic CFT dynamics and associated fast scrambling time play essential role in determining qualitative features...

We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-dimensional surfaces arbitrary genus with an number boundaries. The boundaries are the type relevant in NAdS${}_2$/NCFT${}_1$ correspondence. show that correspond to expansion a certain matrix integral. A key fact is Mirzakhani's recursion relation Weil-Petersson volumes maps directly onto Eynard-Orantin "topological recursion" formulation loop equations this integral provides (non-unique)...

In finite entropy systems, real-time partition functions do not decay to zero at late time. Instead, assuming random matrix universality, suitable averages exhibit a growing "ramp" and "plateau" structure. Deriving this non-decaying behavior in large $N$ collective field description is challenge related one version of the black hole information problem. We describe candidate semiclassical explanation ramp for SYK model holes. SYK, two-replica nonperturbative saddle point fields, with action...

A bstract The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. basic scale in such a system the range over which this behavior persists. We define corresponding time at linearly growing ramp region spectral form factor begins. call t . purpose paper study many-body that display strong chaos, sometimes called scrambling systems. focus on randomly coupled qubit systems, both local and k -local (all-to-all interactions)...

A bstract After averaging over fermion couplings, SYK has a collective field description that sometimes “wormhole” solutions. We study the fate of these wormholes when couplings are fixed. Working mainly in simple model, we find wormhole saddles persist, but new also appear elsewhere integration space — “half-wormholes.” The contributions depend only weakly on specific choice while half-wormhole strongly sensitive. half-wormholes crucial for factorization decoupled systems with fixed they...