Holographic theory of non-invertible gravitational anomalies
Abstract
We review a many-body formulation of gravitational anomalies as obstructions to realizing the complete low-energy data by a local {\it bosonic} lattice quantum system of the same dimension. In this formulation, an anomalous theory can be realized at the boundary of a gapped {\it bosonic} lattice bulk, whose topological order gives a one-to-one classification of the anomaly. An invertible bulk reproduces conventional anomaly inflow; a bulk with non-trivial topological excitations yields a non-invertible generalization. To describe the holographic theory of anomalies, we explain the distinction between uniquely defined topological order and many versions of topological quantum field theory and discuss the boundary-to-bulk map. As an application of the holographic theory of anomalies, we describe morphisms between local quantum theories (such as quantum field theories). These morphisms are built from a bulk domain wall and an invertible boundary junction, which give rise to a sandwich picture. Chiral boson/fermion theory, Laughlin edges, and boundaries of ℤ2 higher gauge theory with bosonic or fermionic point-like excitations illustrate the different kinds of information about non-invertible anomalies contained in transport coefficients, superselection sectors, and condensation data. In particular, a fermionic theory can be viewed as a theory with a particular non-invertible gravitational anomaly. Those examples also reveal that {\it symmetry ∼ gravitational anomaly ∼ topological order in one higher dimension}.
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BibTeX
@misc{wen2026holographic,
title = {{Holographic theory of non-invertible gravitational anomalies}},
author = {Xiao-Gang Wen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15358},
eprint = {2610.15358},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15358},
}
RIS
TY - UNPB
TI - Holographic theory of non-invertible gravitational anomalies
AU - Xiao-Gang Wen
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15358
UR - https://arxiv.org/abs/2610.15358
AB - We review a many-body formulation of gravitational anomalies as obstructions to realizing the complete low-energy data by a local {\it bosonic} lattice quantum system of the same dimension. In this formulation, an anomalous theory can be realized at the boundary of a gapped {\it bosonic} lattice bulk, whose topological order gives a one-to-one classification of the anomaly. An invertible bulk reproduces conventional anomaly inflow; a bulk with non-trivial topological excitations yields a non-invertible generalization. To describe the holographic theory of anomalies, we explain the distinction between uniquely defined topological order and many versions of topological quantum field theory and discuss the boundary-to-bulk map. As an application of the holographic theory of anomalies, we describe morphisms between local quantum theories (such as quantum field theories). These morphisms are built from a bulk domain wall and an invertible boundary junction, which give rise to a sandwich picture. Chiral boson/fermion theory, Laughlin edges, and boundaries of ℤ_2 higher gauge theory with bosonic or fermionic point-like excitations illustrate the different kinds of information about non-invertible anomalies contained in transport coefficients, superselection sectors, and condensation data. In particular, a fermionic theory can be viewed as a theory with a particular non-invertible gravitational anomaly. Those examples also reveal that {\it symmetry ∼ gravitational anomaly ∼ topological order in one higher dimension}.
ER -