Linear response theory and effective action of relativistic hydrodynamics with spin

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)PRVDAQ2470-001010.1103/PhysRevD.96.056012; Phys. Rev. D 96, 079901(A) (2017)PRVDAQ2470-001010.1103/PhysRevD.96.079901; Phys. Rev. D 96, 076016 (2017)PRVDAQ2470-001010.1103/PhysRevD.96.076016; D. Montenegro and G. Torrieri, Phys. Rev. D 100, 056011 (2019)PRVDAQ2470-001010.1103/PhysRevD.100.056011], 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.