Holographic spontaneous parity breaking and emergent hall viscosity and angular momentum

Abstract

We study the spontaneous parity breaking and generating of Hall viscosity and angular momentum in holographic p+ip model, which can describe strongly-coupled chiral superfluid states in many quantum systems. The dual gravity theory, an SU(2) gauge field minimally coupled to Einstein gravity, is parity-invariant but allows a black hole solution with vector hair corresponding to a parity-broken superfluid state. We show that this state possesses a non-vanishing parity-odd transport coefficient -Hall viscosity -and an angular momentum density. We first develop an analytic method to solve this model near the critical regime and to take back-reactions into account. Then we solve the equation for the tensor mode fluctuations and obtain the expression for Hall viscosity via Kubo formula. We also show that a non-vanishing angular momentum density can be obtained through the vector mode fluctuations and the corresponding boundary action. We give analytic results of both Hall viscosity and angular momentum density near the critical regime in terms of physical parameters. The near-critical behavior of Hall viscosity is different from that obtained from a gravitational Chern-Simons model. We find that the magnitude of Hall viscosity to angular momentum density ratio is numerically consistent with being equal to 1/2 at large SU(2) coupling corresponding to the probe limit, in agreement with previous results obtained for various quantum fluid systems and from effective theory approaches. In addition, we find the shear viscosity to entropy density ratio remains above the universal bound.

Torsional response of relativistic fermions in 2 + 1 dimensions

“…[4] gives rise to nonzero angular momentum density but vanishing Hall viscosity, while for the model considered in ref. [22] the ratio between these quantities is compatible with the universal value 1/2 from field theory. In this respect, it may be interesting to note that for a gapped system, such as a free massive Dirac fermion, the spin density of eq.…”

“…Finally, it would be desirable to combine the results from holographic models with those presented here, but it does not appear to be an easy task. The main reason is that there is no unique way to produce Hall viscosity and angular momentum density in holography [4,[21][22][23]. For example, the holographic model considered in ref.…”

Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions

“…Associated transport was explained to be nondissipative and the pertinent transport coefficients were constrained by the second law of thermodynamics or, more generally, from the relevant effective actions [10][11][12][13][14]. In 2+1 dimensions anomalies do not exist, but similar arguments based on the entropy current and partition functions apply, and parity-odd contributions to the hydrodynamic gradient expansion were consistently derived [15][16][17][18][19][20]. One possible term that can be added involves the dissipationless Hall viscosity.…”

Membrane paradigm, gravitational Θ-term and gauge/gravity duality

“…19 Hall viscosity has been studied extensively in the context of Holography, e.g. see [58][59][60][61][62][63][64]69] where C mn is the Cotton-York tensor (4.15). Therefore, following [66], the Θ-term contribution to the energy-momentum tensor of the dual field theory is given by 20…”