Transport coefficient near critical point

• Mohammad Asadi (IPM)

We investigate the time-dependent perturbations of strongly coupled N = 4 SYM theory at finite temperature and at finite chemical potential with a second order phase transition. This theory is modelled by a top-down Einstein-Maxwell-dilaton description which is a consistent truncation of the dimensional reduction of type IIB string theory on AdS5_S5. We focus on spin-1 and spin-2 sectors of perturbations and compute the linearized hydrodynamic transport coefficients up to the third order in gradient expansion. Analytically, we find that all the hydrodynamic quantities have the same critical exponent near the critical point θ = 0.5. Moreover, we conjecture a relation between symmetry enhancement of the underlying theory and vanishing the only third order hydrodynamic transport coefficient λ1 which appears in the shear dispersion relation of a conformal theory on a flat background.