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

## TL;DR

This paper demonstrates that in AdS/BCFT models, the bulk volume decreases along the RG flow, suggesting a potential holographic g-theorem for complexity or fidelity susceptibility analogous to the boundary entropy g-theorem.

## Contribution

The paper proves that bulk volume decreases along RG flows in AdS/BCFT models and proposes a holographic g-theorem for complexity or fidelity susceptibility.

## Key findings

- Bulk volume decreases along RG flow in AdS/BCFT models
- Evidence for a holographic g-theorem for complexity or fidelity susceptibility
- Potential extension of the Affleck-Ludwig g-theorem to holographic complexity

## 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.