Linear response theory and effective action of relativistic hydrodynamics with spin
David Montenegro, Giorgio Torrieri
Abstract
We use linear response techniques to develop the previously proposed relativistic ideal fluid limit with a non-negligible spin density. We confirm previous results [D. Montenegro, Phys. Rev. D 96, 056012 (2017); Phys. Rev. D 96, 079901(A) (2017); Phys. Rev. D 96, 076016 (2017); D. Montenegro and G. Torrieri, Phys. Rev. D 100, 056011 (2019)], obtain expressions for the microscopic transport coefficients using Kubo-like formulas and build up the effective field theory from the computed correlation functions. We verify that for a causal theory with spin the spin-polarization correlator's asymptotic time dependence is the same as for fluctuating hydrodynamics, and investigate backreaction corrections to hydrodynamic variables using a one-loop effective action. We also confirm that polarization makes vortices acquire an effective mass via a mechanism similar to the Anderson-Higgs mechanism in superconductors. As speculated earlier, this could stabilize the ideal hydrodynamic limit against fluctuation-driven vortices.