The breakdown of magneto-hydrodynamics near AdS2 fixed point and energy diffusion bound

We investigate the breakdown of magneto-hydrodynamics at low temperature (T) with black holes whose extremal geometry is AdS(2)xR(2). The breakdown is identified by the equilibration scales (omega(eq), k(eq)) defined as the collision point between the diffusive hydrodynamic mode and the longest-lived non-hydrodynamic mode. We show (omega(eq), k(eq)) at low T is determined by the diffusion constant D and the scaling dimension Delta(0) of an infra-red operator: omega(eq) = 2 pi T Delta(0), k(eq)(2) = omega(eq)/D, where Delta(0) = 1 in the presence of magnetic fields. For the purpose of comparison, we have analytically shown Delta(0) = 2 for the axion model independent of the translational symmetry breaking pattern (explicit or spontaneous), which is complementary to previous numerical results. Our results support the conjectured universal upper bound of the energy diffusion D <= omega(eq)/k(eq)(2) := v(eq)(2) tau(eq) where v(eq) := omega(eq)/k(eq) and tau(eq) := omega(-1)(eq) are the velocity and the timescale associated to equilibration, implying that the breakdown of hydrodynamics sets the upper bound of the diffusion constant D at low T.

Automated summary

In this study, we investigate the breakdown of magneto-hydrodynamics in black holes with extremal geometry AdS(2)xR(2) at low temperature. By examining the diffusion constant and the scaling dimension of an infrared operator, we determine the equilibration scales and provide support for the upper bound of the diffusion constant set by the breakdown of hydrodynamics.