Spin transport coefficients from holography
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The hydrodynamic theory of spin current is a useful tool that can be used to describe different phenomena, ranging from the spin in liquid metal to the global spin polarization in heavy-ion collisions. Recently, exhaustive analyses of spin hydrodynamics have been performed and the constitutive relations are obtained. The spin coefficients that appeared in the constitutive relation are vital to the property of the spin current. The heavy-ion collision involves strong interaction so we can’t obtain these coefficients from the correlation functions in quantum field theory. The holography principle, which implies we may use a classical bulk gravity theory to calculate the correlation functions in strongly coupled boundary quantum field theory, could be a method to calculate these spin transport coefficients. In this paper, we choose a simple vector field model as the holography model. This vector field is dual to the trace of contorsion in the hydrodynamic theory. We performed the calculation at an AdS-Schwartzschild background spacetime and we treat the background value of the vector field as a small number. We constructed the counterterms for the vector field action at the probe limit. We obtained Kubo relations for some spin transport coefficients base on a previous study of spin current hydrodynamics. We calculated these transport coefficients and found them proportional to the slow falloff mode of the vector field.