Fluids, anomalies, and the chiral magnetic effect: A group-theoretic formulation

Abstract

It is possible to formulate fluid dynamics in terms of group-valued variables. This is particularly suited to the cases where the fluid has nonabelian charges and is coupled to nonabelian gauge fields. We explore this formulation further in this paper. An action for a fluid of relativistic particles (with and without spin) is given in terms of the Lorentz and Poincaré (or de Sitter) groups. Considering the case of particles with flavor symmetries, a general fluid action which also incorporates all flavor anomalies is given. The chiral magnetic and chiral vorticity effects as well as the consequences of the mixed gauge-gravity anomaly are discussed.

(Non)-renormalization of the chiral vortical effect coefficient

“…Using this connection, we show that we can understand the numerical value of C from the summation formula ∞ n=1 n = −1/12. (The nonrenormalization in this case can also be inferred from the results in [11], where a different approach based on fluid dynamics in terms of group-valued variables was taken. )…”

Spontaneous chiral symmetry breaking and the chiral magnetic effect for interacting Dirac fermions with chiral imbalance

“…While the universal value of the chiral magnetic conductivity can be formally derived from the low-energy chiral Lagrangian [24][25][26], the role of the chiral chemical potential in this derivation is played by the time derivative of the axion field, which makes its interpretation in the Euclidean finite-temperature path integral formalism quite unclear [9]. In particular, it is not clear how to de-scribe the stationary CME current as a response to static magnetic field in such a framework.…”

Effective actions for anomalous hydrodynamics

“…2 In addition accumulation of evidence from holography [14][15][16] and analysis of free field theories [17] lead to a near-complete picture of anomalous transport induced by flavour anomalies (see also [18,19] for related discussions and [20,21] for general symmetry based group-theoretic approach).…”

“…We follow the conventions described in [30] for non-abelian gauge fields, currents etc. 20 For practical purposes it suffices to think about the stretched horizon and the fields φ I living on spatial sections of a timelike hypersurface straddling the true event horizon.…”

“…On the spatial sections of the horizon we introduce coordinates {φ I }: these will be conflated with the fluid element fields we used to construct our effective action. 20 For completeness let us also record that the temporal direction will be denoted by affine parameter v along the horizon (which goes along for the ride by virtue of adiabaticity).…”