Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?

We study the contour dependence of the out-of-time-ordered correlation function (OTOC) both in weakly coupled field theory and in the Sachdev-Ye-Kitaev (SYK) model. We show that its value, including its Lyapunov spectrum, depends sensitively on the shape of the complex time contour in generic weakly coupled field theories. For gapless theories with no thermal mass, such as SYK, the Lyapunov spectrum turns out to be an exception; their Lyapunov spectra do not exhibit contour dependence, though the full OTOCs do. Our result puts into question which of the Lyapunov exponents computed from the exponential growth of the OTOC reflects the actual physical dynamics of the system. We argue that, in a weakly coupled Phi(4) theory, a kinetic theory argument indicates that the symmetric configuration of the time contour, namely the one for which the bound on chaos has been proven, has a proper interpretation in terms of dynamical chaos. Finally, we point out that a relation between these OTOCs and a quantity which may be measured experimentally - the Loschmidt echo - also suggests a symmetric contour configuration, with the subtlety that the inverse periodicity in Euclidean time is half the physical temperature. In this interpretation the chaos bound reads lambda <= 2 pi/beta=pi T-physical

Two-point function of a d=2 quantum critical metal in the limit kF → ∞, Nf → 0 with NfkF fixed

Theoretical Physic

Constructing the AdS dual of a Fermi liquid: AdS black holes with Dirac hair

Theoretical Physic

Incoherent thermal transport from dirty black holes.

Theoretical Physic

On holographic entanglement entropy of charged matter

098Theoretical Physic

Quantum tunneling dynamics in a complex-valued Sachdev-Ye-Kitaev model quench-coupled to a cool bath

Theoretical Physic

Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder

We compute the direct current resistivity of a scale-invariant, $d$-dimensional strange metal with dynamic critical exponent $z$ and hyperscaling-violating exponent $\theta$, weakly perturbed by a scalar operator coupled to random-field disorder that locally breaks a $\mathbb{Z}_2$ symmetry. Independent calculations via Einstein-Maxwell-Dilaton holography and memory matrix methods lead to the same results. We show that random field disorder has a strong effect on resistivity: charge carriers in the infrared are easily depleted, as the relaxation time for momentum is surprisingly small. In the course of our holographic calculation we use a non-trivial dilaton coupling to the disordered scalar, allowing us to study a strongly-coupled scale invariant theory with $\theta \ne 0$. Using holography, we are also able to determine the disorder strength at which perturbation theory breaks down. Curiously, for locally critical theories this breakdown occurs when the resistivity is proportional to the entropy density, up to a possible logarithmic correction.Comment: 20 pages. v2: minor changes, more references. v3: published versio