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Paper IPM / Physic / 16052  


Abstract:  
In the ComplexityAction (CA) proposal there are two different methods to regularize the gravitational onshell action, which are equivalent in the framework of AdS/CFT. In this paper, we want to study the equivalence of them in the context of AdS/BCFT. To do so, we consider a thermal BCFT state in two dimensions which is dual to a twosided BTZ black hole excised by a dynamical ETW brane. We show that if one includes the timelike counterterms inspired by holographic renormalization as well as the GibbonsHawkingYork term on the timelike boundary of the WDW patch, which exists in one of the regularizations, the coefficients of the UV divergent terms of actioncomplexity in the two methods become equal to each other.
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