Many-body chaos and energy dynamics in holography

It is well-known that chiral anomaly can be macroscopically detected through energy and charge transport, due to chiral magnetic effect. On the other hand, the chaotic modes in a many body system are only associated with energy conservation. So, this suggests that, perhaps, one can detect the microscopic anomalies through the quantum chaos in such systems. To holographically investigate this idea, we consider a magnetized brane in AdS space time with a Chern-Simons coupling in the bulk. By studying the shock wave geometry in this background, we first compute the corresponding butterfly velocities, in the presence of an external magnetic field B, in µ T and B T 2 limit. We find that the butterfly propagation in the direction of B has not the same velocity as the one of opposite direction; the difference is turned out to be as ∆v B = (log(4) − 1)∆v sound with ∆v sound being the difference between velocity of the two sound modes propagating in the system. Such special form of splitting confirms the idea that chiral anomaly can be macroscopically manifested via quantum chaos. We then show that the pole-skipping points of energy density Green's function in the boundary theory coincide precisely with the chaos points. This might be regarded as hydrodynamic origin of quantum chaos in an anomalous system. In addition, by studying the near horizon dynamics of a scalar field on the above background, we find the spectrum of pole-skipping points associated with the two-point function of dual boundary operator. We show that the sum of wavenumbers corresponding to the pole-skipping points at a specific Matsubara frequency follows from a closed formula. Interestingly, we find that the same information about splitting of butterfly velocities is encoded in the pole-skipping points with the lowest Matsubara frequency, independent of scaling dimension of dual boundary operator. * abbasi@lzu.edu.cn † smjty25@gmail.com 4 See also [36] for the first study of pole-skipping at finite coupling. 5 Let us denote that by using symmetries, we only work with a subset of δg µν 's. 6 v is the time coordinate in the Eddington-Finkelstein coordinates.

Section: Pole-skipping Of Energy Density Green's Function From Hologrmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 85%

See 1 more Smart Citation

Quantum chaos, pole-skipping and hydrodynamics in a holographic system with chiral anomaly

Abbasi

Tabatabaei

2020

“…To elucidate the key ideas of [17] as well as [11] that are relevant to our discussion of pole-skipping, we will first consider a minimally coupled scalar field ϕ in the uncorrected background, i.e. AdS 5 black brane 2 , ds 2 = −r 2 f (r)dv 2 + 2dvdr + r 2 (dx 2 + dy 2 + dz 2 ).…”

Section: Review Of Key Ideasmentioning

confidence: 99%

“…In [10], this pole-skipping phenomenon was also explained in terms of the shift symmetry of an effective hydrodynamic description. The pole-skipping was also analytically studied in [11] as an universal behavior near the horizon where the timetime component of the Einstein equation (in ingoing Eddington-Finkelstein coordinates) vanishes such that the dual retarded two point function is not uniquely defined. The poleskipping phenomenon has also been checked to hold for SYK system [12] and 2D CFT with large central charge [13].…”

Section: Introductionmentioning

confidence: 99%

Higher curvature corrections to pole-skipping

Xing

2019

Recent developments have revealed a new phenomenon, i.e. the residues of the poles of the holographic retarded two point functions of generic operators vanish at certain complex values of the frequency and momentum. This so-called pole-skipping phenomenon can be determined holographically by the near horizon dynamics of the bulk equations of the corresponding fields. In particular, the pole-skipping point in the upper half plane of complex frequency has been shown to be closed related to many-body chaos, while those in the lower half plane also places universal and nontrivial constraints on the two point functions. In this paper, we study the effect of higher curvature corrections, i.e. the stringy correction and Gauss-Bonnet correction, to the (lower half plane) pole-skipping phenomenon for generic scalar, vector, and metric perturbations. We find that at the poleskipping points, the frequencies ω n = −i2πnT are not explicitly influenced by both R 2 and R 4 corrections, while the momenta k n receive corresponding corrections.H. Corrections to k 1 in three channels of metric perturbations 30 -2 -Recently, the near horizon analysis is generalized in [17] to equations of bulk fields dual to spin-0, spin-1 and spin-2 operators, and pole-skipping is found to exist in retarded two point functions of these operators. However, these pole-skipping points appear in the lower half plane of the complex frequency, in contrast to the aforementioned pole-skipping point of chaos located in the upper half plane at ω = +i2πT . This indicates that pole-skipping may not always be directly related to quantum chaos, but could be a consequence of a more general feature of near horizon bulk equations. Relevant discussions can also be found in [18,19,20].where A and B are coefficients in the asymptotic expansion of the scalar field near the boundary φ → Ar ∆−4 + Br −∆ .(2.5) 2 In this paper, the AdS radius is always set to unity for convenience. 3 One may well consider the equivalent form ∇µ∇ µ ϕ − m 2 ϕ = 0. Note in that case, the near horizon expansion of the perturbation equation would in general be different at each order due to the extra √ −g factor. Of course, the physics will remain the same. Here we simply follow the convention used in [17] for the sake of comparison.11 Note that at λGB = 1/4, N 2 GB = 1/2, the shear viscosity vanishes, and the theory exhibits unusual properties in many aspects, such as quasinormal modes and thermodynamics, see [54,59,60] for detailed discussions. Since this value lies far outside of the causality range (4.3), we will not consider it in the following.

On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections

Grozdanov

2019

Self Cite

103

Pole-skipping is a recently discovered signature of many-body quantum chaos in collective energy dynamics. It establishes a precise connection between resummed, allorder hydrodynamics and the underlying microscopic chaos. In this paper, we demonstrate the existence of pole-skipping in holographic conformal field theories with higherderivative gravity duals. In particular, we first consider Einstein-Hilbert gravity deformed by curvature-squared (R 2 ) corrections and then type IIB supergravity theory with the α 3 R 4 term, where α is set by the length of the fundamental string. The former case allows us to discuss the effects of leading-order 1/N c corrections (with N c being the number of colours of the dual gauge group) and phenomenological coupling constant dependence. In Einstein-Gauss-Bonnet theory, pole-skipping turns out to be valid non-perturbatively in the Gauss-Bonnet coupling. The α 3 R 4 deformation enables us to study perturbative inverse 't Hooft coupling corrections (α 3 ∼ 1/λ 3/2 ) in SU (N c ), N = 4 supersymmetric Yang-Mills theory with infinite N c . While the maximal Lyapunov exponent characterising quantum chaos remains uncorrected, the butterfly velocity is shown to depend both on N c and the coupling. Several implications of the relation between hydrodynamics and chaos are discussed, including an intriguing similarity between the dependence of the butterfly velocity and the ratio of shear viscosity to entropy density on stringy corrections.