PIRSA:17110138 Scientific Series Quantum Fields and Strings

DOI10.48660/17110138

Series: Quantum Fields and Strings

Hellerman, S. (2017). Quantum Information Theory of the Gravitational Anomaly. Perimeter Institute. https://pirsa.org/17110138

Hellerman, Simeon. Quantum Information Theory of the Gravitational Anomaly. Perimeter Institute, Nov. 21, 2017, https://pirsa.org/17110138 

@misc{ pirsa_PIRSA:17110138,
  doi = {10.48660/17110138},
  url = {https://pirsa.org/17110138},
  author = {Hellerman, Simeon},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Quantum Information Theory of the Gravitational Anomaly},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {nov},
  note = {PIRSA:17110138 see, \url{https://pirsa.org}}
}

Abstract

In this talk I prove 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.  I make this precise by combining 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 QFT:

    No continuum quantum field theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes.

I also show that the conclusion can be generalized to six dimensions by dimensional reduction on a four-manifold of nonvanishing signature.  I will advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information.

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