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

Abstract

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.

Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography

“…Having this interesting connection between four-point OTOC and pole-skipping phenomena in two-point function of energy density T 00 , it is natural to ask if there is a similar connection and interesting relevant physics for fields other than T 00 . In particular, the pole-skipping points for scalar and Maxwell fields in flat space were computed in [30][31][32][33][34][35] by an exact calculation of G R (ω, k) or by a near-horizon analysis. However, in contrast to the pole-skipping of energy density, the relation between the behavior of four point functions and the pole-skipping points for the two point function of bulk scalar and Maxwell fields is not well-studied.…”

“…z→1 −) in the last line where we only extract the finite terms, of order (1 − z) 0 35. The Pochhammer symbol is defined as (x) j ≡ Γ(x+j) Γ(x) = (x + j − 1)• • • (x + 1) • (x) for integer j.If N is a non-integer (N → n):2 F 1 (a, b; a + b + n; z) = Γ(a + b + n)Γ(n) Γ(a + n)Γ(b + n) ∞ k=0 (a) k (b) k (1 − n) k k!…”

“…Note that we should be careful when Re(α) ≤ 0. We leave this case as future work 35. In the cases where N is zero or a negative integer, we also discarded regular terms which are not relevant to the pole-skipping structure.…”

Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential

“…However the resultant pole-skipping points in such cases lie totally in the lower half of Imw − Imq plane. See also[64][65][66][67][68][69][70][71][72][73][74].…”

Classifying pole-skipping points

“…The existence of pole-skipping for fermions was confirmed in [17]. Other recent development involving pole-skipping include for instance [18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In all the above examples, pole-skipping was studied for boundary theories living in a flat spacetime, where one can decompose the bulk perturbations and the boundary Green's function in terms of plane waves.…”