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Paper   IPM / P / 16051
School of Physics
  Title:   Regularizations of action-complexity for a pure BTZ black hole microstate
  Author(s):  F. Omidi
  Status:   Published
  Journal: JHEP
  Vol.:  07
  Year:  2020
  Pages:   020
  Supported by:  IPM
In the Complexity-Action (CA) proposal there are two different methods to regularize the gravitational on-shell 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 two-sided 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 Gibbons-Hawking-York term on the timelike boundary of the WDW patch, which exists in one of the regularizations, the coefficients of the UV divergent terms of action-complexity in the two methods become equal to each other.

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