Quantum Information Theory of the Gravitational Anomaly

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.

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Tuesday, November 21, 2017 - 14:30 to 16:00
Location: 
Space Room
Room #: 
400