Entanglement Entropy on Fuzzy Spaces

Details Entanglement Entropy on Fuzzy Spaces Entanglement Entropy on Fuzzy Spaces

2006-04-29

arxiv.org/abs/gr-qc/0605003v3

Phys.Rev.D74:044014,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 4 figures. This research is dedicated to Rafael Sorkin on the occasion of his 60th birthday

Scientific paper

10.1103/PhysRevD.74.044014

We study the entanglement entropy of a scalar filed in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom. In the Moyal plan limit of the fuzzy disc the entanglement entropy per unit area (length) diverges if the ignored region is of infinite size. The divergence is (interpreted) of IR-UV mixing origin. In general we expect the entanglement entropy per unit area to be finite on a non-commutative space if the ignored region is of finite size.

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