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

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