Boundaries, Lattices and the Gravitational Anomaly (京都)

Abstract

I discuss a general proof of the following two facts regarding two-dimensional local quantum field theories with non-vanishing gravitational anomaly:

1. these theories do not admit a lattice regularization (this generalizes the renowned Nielsen-Ninomiya theorem);
2. their Hilbert space does not factorize into Hilbert spaces in complementary regions. Fact 2 implies in particular that, in the presence of a non-vanishing gravitational anomaly, the usual definitions of quantum entanglement break down.