Anomalies and time reversal invariance in relativistic hydrodynamics: the second order and higher dimensional formulations

By D. Kharzeev, Ho-Ung Yee. 2011

141 citations recorded by the source corpus.

We present two new results on relativistic hydrodynamics with anomalies and external electromagnetic fields, “Chiral MagnetoHydroDynamics” (CMHD). First, we study CMHD in four dimensions at second order in the derivative expansion assuming the conformal/Weyl invariance. We classify all possible independent conformal second order viscous corrections to the energy-momentum tensor and to the U(1) current in the presence of external electric and/or magnetic fields, and identify eighteen terms that originate from the triangle anomaly. We then propose and motivate the following guiding principle to constrain the CMHD: the anomaly–induced terms that are even under the time reversal invariance should not contribute to the local entropy production rate. This allows us to fix thirteen out of the eighteen transport coefficients that enter the second order formulation of CMHD. We also relate one of our second order transport coefficients to the chiral shear waves. Our second subject is hydrodynamics with (N + 1)-gon anomaly in an arbitrary 2N dimensions. The effects from the (N + 1)-gon anomaly appear in hydrodynamics at (N − 1)’th order in the derivative expansion, and we identify precisely N such corrections to the U(1) current. The time reversal constraint is powerful enough to allow us to find the analytic expressions for all transport coefficients. We confirm the validity of our results (and of the proposed guiding principle) by an explicit fluid/gravity computation within the AdS/CFT correspondence.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0a44a88be0f15c9fa283f62065211fbd0d2c3c0f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

Parity-violating hydrodynamics in 2 + 1 dimensions (2011, background): “For considerations of hydrodynamics in arbitrary dimensions see [32,49].”
Mapping the phases of quantum chromodynamics with beam energy scan (2019, background): “Finally the σ5 is time-reversal even [116] which implies the non-dissipative nature of the CME transport current.”
Notes on Anomaly Induced Transport (2016, background): “Higher orders in derivatives have been studied in [43, 44].”
Anomaly inflow and thermal equilibrium (2013, methodology): “It matches the anomaly-induced current and stress tensor computed using entropy arguments [10, 11] or using the hydrostatic generating functional [39].”
Constraints on fluid dynamics from equilibrium partition functions (2012, background): “Our main aim in this section is twofold - first is to carry through in arbitrary dimensions this program of equilibrium partition function thus generalising the results of [47, 48] and re deriving in a path-integral friendly language the results of [8, 46].”
Adiabatic hydrodynamics: the eightfold way to dissipation (2015, background): “We now have clear picture of how to derive the constraints on them using the equilibrium partition function [3, 9–13] (for related work on anomaly induced transport we refer the reader to [14–35]).”