Spin polarization in the strongly interacting QCD matter at global and local equilibrium

We develop a new technique to compute expectation values in a free-field theory at global equilibrium with non-vanishing vorticity. This technique is applied to obtain the exact polarization vector of particles of any spin, to all orders in thermal vorticity. We also study relativistic fluids at local equilibrium and compute the first-order contribution to spin polarization of Dirac fermions from the gradients of temperature. The symmetric derivative of the four-temperature, the so-called thermal shear, is found to yield a significant contribution to polarization, and it is able to accommodate the discrepancy between theory and experiments, solving the longstanding ``Polarization sign puzzle''.