Holographic Complexity as a Probe of Boundary Entropy in AdS/BCFT
Abstract
We investigate how the sewing operations familiar from topological quantum field theory provide a useful organizational framework for semiclassical AdS/BCFT path integrals. Our purpose is not to identify AdS/BCFT with a topological field theory: the bulk geometry, the end-of-the-world brane, and the on-shell action remain intrinsically metric-dependent. Rather, we use the TQFT language of state preparation, orientation reversal, and gluing to separate interface data from local geometric contributions. For AdS3/BCFT2, we review how the Euclidean on-shell action and the Ryu--Takayanagi prescription reproduce the Affleck--Ludwig boundary entropy log g after holographic renormalization. We then formulate the Complexity=Action calculation in the presence of an end-of-the-world brane, carefully distinguishing bulk, brane, joint, and null-boundary contributions. We emphasize that finite terms in a relative Wheeler--DeWitt action depend on the choice of regulator matching and on the null-boundary counterterm scheme unless their scheme independence is established explicitly. Finally, we extend the geometric construction to a planar BTZ background and derive the brane embedding from the Neumann boundary condition. The resulting framework clarifies which aspects of holographic complexity are sensitive to boundary conditions and which require further renormalization input before they can be interpreted as universal boundary data.
Versions
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BibTeX
@misc{santos2026holographic,
title = {{Holographic Complexity as a Probe of Boundary Entropy in AdS/BCFT}},
author = {Fabiano F. Santos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.10348},
eprint = {2608.10348},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10348},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Holographic Complexity as a Probe of Boundary Entropy in AdS/BCFT
AU - Fabiano F. Santos
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2608.10348
UR - https://arxiv.org/abs/2608.10348
AB - We investigate how the sewing operations familiar from topological quantum field theory provide a useful organizational framework for semiclassical AdS/BCFT path integrals. Our purpose is not to identify AdS/BCFT with a topological field theory: the bulk geometry, the end-of-the-world brane, and the on-shell action remain intrinsically metric-dependent. Rather, we use the TQFT language of state preparation, orientation reversal, and gluing to separate interface data from local geometric contributions. For AdS_3/BCFT_2, we review how the Euclidean on-shell action and the Ryu--Takayanagi prescription reproduce the Affleck--Ludwig boundary entropy log g after holographic renormalization. We then formulate the Complexity=Action calculation in the presence of an end-of-the-world brane, carefully distinguishing bulk, brane, joint, and null-boundary contributions. We emphasize that finite terms in a relative Wheeler--DeWitt action depend on the choice of regulator matching and on the null-boundary counterterm scheme unless their scheme independence is established explicitly. Finally, we extend the geometric construction to a planar BTZ background and derive the brane embedding from the Neumann boundary condition. The resulting framework clarifies which aspects of holographic complexity are sensitive to boundary conditions and which require further renormalization input before they can be interpreted as universal boundary data.
ER -