Abstract
We explore the role of torsion as source of spin current in strongly interacting conformal fluids using holography. We establish the constitutive relations of the basic hydrodynamic variables, the energy-momentum tensor and the spin current based on the classification of the spin sources in irreducible Lorentz representations. The fluids we consider are assumed to be described by the five dimensional Lovelock-Chern-Simons gravity with independent vielbein and spin connection. We construct a hydrodynamic expansion that involves the stress tensor and the spin current and compute the corresponding one-point functions holographically. As a byproduct we find a class of interesting analytic solutions to the Lovelock-Chern-Simons gravity, including blackholes, by mapping the equations of motion into non-linear algebraic constraints for the sources. We also derive a Lee-Wald entropy formula for these blackholes in Chern-Simons theories with torsion. The blackhole solutions determine the thermodynamic potentials and the hydrodynamic constitutive relations in the corresponding fluid on the boundary. We observe novel spin induced transport in these holographic models: a dynamical version of the Barnett effect where vorticity generates a spin current and anomalous vortical transport transverse to a vector-like spin source.
Highlights
Hydrodynamic description of strongly correlated systems with spin degrees of freedom is an important open problem with various applications ranging from condensed matter to astrophysics and high energy physics [1,2,3,4,5]
We establish the constitutive relations of the basic hydrodynamic variables, the energy-momentum tensor and the spin current based on the classification of the spin sources in irreducible Lorentz representations
We summarize the coupling between spin sources and the hydrodynamic components of the spin current in the following table: 3.3 Hydrodynamic degrees of freedom
Summary
Hydrodynamic description of strongly correlated systems with spin degrees of freedom is an important open problem with various applications ranging from condensed matter to astrophysics and high energy physics [1,2,3,4,5]. Where T μν is the canonical energy momentum tensor obtained from Noether’s theorem as the charge under space-time translations and Sλμν is the relativistic generalization of Sijk i.e. the current in the ith direction of spin orthogonal to the j, k plane. Even though the latter is supposedly present whenever the quantum fields transform non-trivially under rotations, its value changes under the following pseudo-gauge transformation [20]. Appendix C contains, as far as we know, a novel derivation of the Wald entropy formula for Chern-Simons theories with nontrivial torsion
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