Universality of anomalous conductivities in theories with higher-derivative holographic duals

Abstract

Anomalous chiral conductivities in theories with global anomalies are independent of whether they are computed in a weakly coupled quantum (or thermal) field theory, hydrodynamics, or at infinite coupling from holography. While the presence of dynamical gauge fields and mixed, gauge-global anomalies can destroy this universality, in their absence, the non-renormalisation of anomalous Ward identities is expected to be obeyed at all intermediate coupling strengths. In holography, bulk theories with higherderivative corrections incorporate coupling constant corrections to the boundary theory observables in an expansion around infinite coupling. In this work, we investigate the coupling constant dependence and universality of anomalous conductivities (and thus of the anomalous Ward identities) in general, four-dimensional systems that possess asymptotically anti-de Sitter holographic duals with a non-extremal black brane in five dimensions, and anomalous transport introduced into the boundary theory via the bulk Chern-Simons action. We show that in bulk theories with arbitrary gauge-and diffeomorphism-invariant higher-derivative actions, anomalous conductivities, which can incorporate an infinite series of (inverse) coupling constant corrections, remain universal. Owing to the existence of the membrane paradigm, the proof reduces to a construction of bulk effective theories at the horizon and the boundary. It only requires us to impose the condition of horizon regularity and correct boundary conditions on the fields. We also discuss ways to violate the universality by violating conditions for the validity of the membrane paradigm, in particular, by adding mass to the vector fields (a case with a mixed, gauge-global anomaly) and in bulk geometries with a naked singularity.

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

“…In the strongest universal statement to date, by following the observation of [21] that the anomalous chiral magnetic conductivity can also be computed from a horizon formula, Ref. [22] proved the universality of four anomalous chiral conductivities to all orders in the inverse coupling expansion, i.e. in any classical higher-derivative bulk theory, given certain conditions specified in [22].…”

“…[22] proved the universality of four anomalous chiral conductivities to all orders in the inverse coupling expansion, i.e. in any classical higher-derivative bulk theory, given certain conditions specified in [22].…”

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

“…Equation (2.48) is linking between two separate regimes of scales; first, the hydrodynamic regime ω T and second, the scales ω ∼ T which are more relevant to chaos. Following [59], it would be interesting to investigate whether such feature will be protected at finite coupling.…”

Dynamical gauge fields and anomalous transport at strong coupling

“…Eventually the universality of the CME, CVE and CSE coefficients in holography based on two-derivative gravity was established in [23] where they are linked to smooth near-horizon geometry of the corresponding black hole solutions 4 . This holographic demonstration was later extended to higher derivative gravity theories in [24].…”

“…This condition allow us to equate σ AV and σ V A , thus the vector one point function carries all the information regarding the CME, CSE and CVE conductivities. Alternatively one can obtain the conductivities from the linear response of the one-point functions to the magnetic like sources [23,24], which is the route we take in this work. In particular we read off the vector like conductivities from the linear response of the one-point function J V ,…”