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Paper   IPM / Physic / 15694
School of Physics
  Title:   On the Role of Counterterms in Holographic Complexity
1.  A. Akhavan
2.  F. Omidi
  Status:   Published
  Journal: JHEP
  Vol.:  11
  Year:  2019
  Pages:   054
  Supported by:  IPM
We consider the Complexity=Action (CA) proposal, in Einstein gravity, and investigate counterterms which are able to remove all the UV divergences of holographic complexity. To study the UV divergences, one can apply two different methods of regularizations. It has been proved [22, 23] that the coefficients of the UV divergences are not equal in both regularizations. We show that if one considers the Gibbons-Hawking-York term as well as new types of counterterms inspired from holographic renormalization on timelike boundaries of the WDW patch, the coefficients on both sides match very well. Next, we introduce new counterterms on the null boundaries of the WDW patch for four and five dimensional asymptotically AdS spacetimes which are able to remove all the UV divergences of the on- shell action. Moreover, they are covariant and do not change the equations of motion. At the end, we calculate them for an AdS-Schwarzschild black hole.

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