2021/01/09 by Simeon Hellerman, Hellerman, Simeon, Domenico Orlando +3 · 11 citations
Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #FOS: Physical sciences #Gravitation #Gravitational anomaly #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.48550/arxiv.2101.03320
published in arXiv (Cornell University) (Cornell University) · 60 pages, 6 figures
arxiv created 2021/01/09 · openalex publication_date 2021/01/09 · arxiv updated 2021/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the standard notion of entanglement is not defined for gravitationally anomalous two-dimensional theories because they do not admit a local tensor factorization of the Hilbert space into local Hilbert spaces. Qualitatively, the modular flow cannot act consistently and unitarily in a finite region, if there are different numbers of states with a given energy traveling in the two opposite directions. We make this precise by decomposing it into two observations: First, a two-dimensional CFT admits a consistent quantization on a space with boundary only if it is not anomalous. Second, a local tensor factorization always leads to a definition of consistent, unitary, energy-preserving boundary condition. As a corollary we establish a generalization of the Nielsen-Ninomiya theorem to all two-dimensional unitary local QFTs: No continuum quantum field theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes. We also show that the conclusion can be generalized to six dimensions by dimensional reduction on a four-manifold of nonvanishing signature. We advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information.