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Anomalies and entanglement entropy

Entanglement entropy is a measure of the degree of correlation between subspaces of a given state. When considering the vacuum state of quantum field theory, the entanglement entropy of such a state is usually associated with a partitioning of space into an interior and exterior, the entanglement entropy measuring the degree of correlation along the interface in the vacuum. 

Since the vacuum is invariant under boosts one expects that the entanglement entropy will also be invariant under boosts and this is, indeed, usually the case. However, for certain quantum field theories, boost invariance can be anomalous. An anomalous symmetry is a symmetry which is broken by quantum mechanical effects. Such anomalies typically arise if the theory possesses an imbalance of chiral fermions. 

In a recent paper, Amos Yarom and Tatsuma Nishioka, have shown that in the presence of anomalies the entanglement entropy is not invariant under boosts. Moreover, the non boost invariance of the entanglement entropy can be characterised in a unique way such that its behaviour can be computed independently of the detailed description of the system. In this sense the contribution of anomalies to entanglement entropy can be considered to be universal.

An anomalous propulsion mechanism

Noether’s theorem relates symmetries to conservation laws. In a classical theory, a symmetry of the action implies an associated conserved charge. This relation does not necessarily hold in a quantum theory. Indeed, a the violation of what would seem like a symmetry of the theory due to quantum effects is referred to as an anomaly. In a recent paper, E. Shaverin and A. Yarom have argued that such a quantum mechanical effect should be made visible at a macroscopic level. In particular, they consider a gas of particles whose dynamics are governed by an anomalous theory, and which is trapped inside a spherical rotating shell. If the gas is instantaneously released from the shell then the anomaly would force the emission of the gas to be directional which implies, via momentum conservation that the shell will be propelled forward. This is an instance were a subtle quantum mechanical effect has a large scale manifestation.

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