A complexity/fidelity susceptibility g-theorem for AdS${}_3$/BCFT${}_2$

Abstract

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.

24 pages, 4 figures v2: added citations and minor clarifications

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Cited by in corpus (43)

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• Holographic Complexity Equals Which Action?
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• Renormalized Circuit Complexity
• Cosmological Complexity
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• Holographic complexity of black non-susy D3-brane and the high temperature limit
• On Complexity of Holographic Flavors
• Holographic and QFT Complexity with angular momentum