Holographic Complexity as a Probe of Boundary Entropy in AdS/BCFT

Abstract

This work establishes a formal bridge between the organizational principles of TQFTs and the AdS/BCFT correspondence, interpreting end of the world EOW branes as physical interfaces carrying boundary-state data. By developing a dictionary that maps cobordism composition to holographic sewing, we show that the Euclidean action and the Ryu and Takayanagi prescription consistently isolate the universal boundary entropy (log g). Applying the Complexity-Action proposal, we demonstrate that a relative renormalization prescription extracts this same universal contribution from the Wheeler and DeWitt action. Finally, we extend the analysis to BTZ black holes, where the late-time complexity growth is shown to encode both the thermal interior dynamics and the universal information of the boundary conditions via the brane tension.