Holographic Reconstruction from Broken Conformal Gauge Symmetry
Abstract
We investigate bulk--boundary structures in AdS4/CFT3 from the viewpoint of gravity as a broken phase of conformal gauge symmetry. A crucial distinction is made between the Euler and Pontryagin characteristic classes. The gauge-theoretic gravitational action contains an Euler sector, whose total-derivative representation gives a boundary form depending on both intrinsic and extrinsic geometry. This structure is different from the Pontryagin descent to the three-dimensional gravitational Chern--Simons functional, whose metric variation gives the Cotton tensor and underlies the mixed boundary conditions studied by de Haro. We perform a Fefferman--Graham expansion of the Euler boundary form in asymptotically AdS4 spacetime. The normalizable coefficient g(3)ij does not contribute linearly to the finite Euler boundary term: its contribution from the cubic extrinsic- curvature sector vanishes by Tr g(3)=0, while curvature-- extrinsic-curvature terms containing g(3) vanish at the conformal boundary. A direct Codazzi analysis additionally shows that the Cotton tensor appears in the asymptotic mixed curvature but its contribution through the tangential-connection boundary variation vanishes for standard Dirichlet data. This indicates two distinct types of bulk--boundary structure: a global/topological Euler relation and a local Pontryagin--Cotton relation. We distinguish this kinematic Cotton appearance from a finite Cotton boundary response and discuss the implications for holographic reconstruction.
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BibTeX
@misc{fukuyama2026holographic,
title = {{Holographic Reconstruction from Broken Conformal Gauge Symmetry}},
author = {Takeshi Fukuyama},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27511},
eprint = {2610.27511},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27511},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Holographic Reconstruction from Broken Conformal Gauge Symmetry
AU - Takeshi Fukuyama
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27511
UR - https://arxiv.org/abs/2610.27511
AB - We investigate bulk--boundary structures in AdS_4/CFT_3 from the viewpoint of gravity as a broken phase of conformal gauge symmetry. A crucial distinction is made between the Euler and Pontryagin characteristic classes. The gauge-theoretic gravitational action contains an Euler sector, whose total-derivative representation gives a boundary form depending on both intrinsic and extrinsic geometry. This structure is different from the Pontryagin descent to the three-dimensional gravitational Chern--Simons functional, whose metric variation gives the Cotton tensor and underlies the mixed boundary conditions studied by de Haro. We perform a Fefferman--Graham expansion of the Euler boundary form in asymptotically AdS_4 spacetime. The normalizable coefficient g_(3)ij does not contribute linearly to the finite Euler boundary term: its contribution from the cubic extrinsic- curvature sector vanishes by Tr g_(3)=0, while curvature-- extrinsic-curvature terms containing g_(3) vanish at the conformal boundary. A direct Codazzi analysis additionally shows that the Cotton tensor appears in the asymptotic mixed curvature but its contribution through the tangential-connection boundary variation vanishes for standard Dirichlet data. This indicates two distinct types of bulk--boundary structure: a global/topological Euler relation and a local Pontryagin--Cotton relation. We distinguish this kinematic Cotton appearance from a finite Cotton boundary response and discuss the implications for holographic reconstruction.
ER -