Surface Counterterms and Regularized Holographic Complexity

Understand

The holographic complexity is UV divergent.

• As a finite complexity, we propose a "regularized complexity" by employing a similar method to the holographic renormalization.
• We add codimension-two boundary counterterms which do not contain any boundary stress tensor information.
• It means that we subtract only non-dynamic background and all the dynamic information of holographic complexity is contained in the regularized part.