Recent experimental observation of spin polarization of hadrons in relativistic heavy-ion collisions [1] motivates the development of the theory describing spin transport in relativistic plasma. In this talk, I will introduce our recent work on a theoretical formulation of relativistic spin hydrodynamics based on the second law of local thermodynamics and linear response theory [2]. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient, the rotational viscosity. Using the derived constitutive relation, I will explain our main results; an interesting mode mixing phenomenon between the transverse shear and the spin density modes, and several field-theoretical ways to compute the rotational viscosity via the Green-Kubo formula based on retarded correlation functions.

References:
[1] STAR Collaboration, L. Adamczyk et al., Nature 548 (2017) 62?65, arXiv:1701.06657 [nucl-ex]
[2] M. Hongo, X-G. Huang, M. Kaminski, M. Stephanov, H-U Yee, arXiv:2107.14231 [hep-th]