2019-07-12 11:00  P7F

Momentum-space entanglement in scalar field theory on fuzzy spheres

Shoichi Kawamoto

We consider the entanglement in momentum space for scalar field theory on the fuzzy two-sphere. This field theory can be regarded as a toy-model of quantum gravity (QFT on a noncommutative spacetime as a simple model of quantum geometry) and it is known to exhibit a peculiar phenomenon, the UV/IR mixing; the ultraviolet divergence is related to the infrared singularity of the theory. The scalar field theory can be described by a matrix model, and we study the entanglement for high and low momentum (or energy) modes of this matrix model by perturbation theory. The entanglement entropy with respect to the bipartite momentum space is considered and the UV/IR mixing phenomenon is discussed in terms of the entanglement of different degrees of freedom.