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Paper IPM / P / 16315  


Abstract:  
We employ the âcomplexity equals action" conjecture to investigate the action growth rate for charged and neutral AdS black branes of a holographic toy model consisting of EinsteinMaxwell theory in d + 1dimensional bulk spacetime with d1 massless scalar fields which is called EinsteinMaxwellAxion (EMA) theory. From the holographic point of view, the scalar fields source a spatially dependent field theory with momentum relaxation on the boundary, which is dual to the homogeneous and isotropic black branes. We find that the growth rate of holographic complexity within the WheelerDeWitt (WDW) patch is finite for
these solutions at the late time limit. In fact, the momentum relaxation term does not affect the previous results explicitly but changes the value of the mass and provides strong motivations to investigate the vanishing of complexity growth rate at some finite temperature other than zero. Also, we study nonlinear contribution of axion field kinetic term in the context of kessence model in fourdimensional spacetime. We find that in the study of full time dependence, by increasing the coupling of nonlinear term, the action growth rate decreases while at late time limit, this modification does not change the growth rate apart from the mass definition.
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