T(T)over-bar-Deformed Conformal Field Theories out of Equilibrium

We consider the out-of-equilibrium transport in T (T) over bar -deformed (1 + 1)-dimension conformal field theories (CFTs). The theories admit two disparate approaches, integrability and holography, which we make full use of in order to compute the transport quantities, such as the exact nonequilibrium steady state currents. We find perfect agreements between the results obtained from these two methods, which serve as nontrivial checks of the T (T) over bar -deformed holographic correspondence from the dynamical standpoint. It turns out that integrability also allows us to compute the momentum diffusion, which is given by a universal formula. We also remark on an intriguing connection between the T (T) over bar -deformed CFI's and reversible cellular automata.