In BCFT, boundary complexity increments show the same divergent structure for volume, action, and path-integral measures in d>2, but in d=2 the action measure gives a finite constant instead of a logarithmic divergence.
A complexity/fidelity susceptibility g-theorem for AdS$_3$/BCFT$_2$
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We use a recently proposed holographic Kondo model as a well-understood example of AdS/boundary CFT (BCFT) duality, and show explicitly that in this model the bulk volume decreases along the RG flow. We then obtain a proof that this volume loss is indeed a generic feature of AdS/BCFT models of the type proposed by Takayanagi in 2011. According to recent proposals holographically relating bulk volume to such quantities as complexity or fidelity susceptibility in the dual field theory, this suggests the existence of a complexity or fidelity susceptibility analogue of the Affleck-Ludwig g-theorem, which famously states the decrease of boundary entropy along the RG flow of a BCFT. We comment on this possibility.
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Does Boundary Distinguish Complexities?
In BCFT, boundary complexity increments show the same divergent structure for volume, action, and path-integral measures in d>2, but in d=2 the action measure gives a finite constant instead of a logarithmic divergence.