Entanglement entropy on the fuzzy sphere

Understand

We obtain entanglement entropy on the noncommutative (fuzzy) two-sphere.

• To define a subregion with a well defined boundary in this geometry, we use the symbol map between elements of the noncommutative algebra and functions on the sphere.
• We find that entanglement entropy is not proportional to the length of the region's boundary.
• Rather, in agreement with holographic predictions, it is extensive for regions whose area is a small (but fixed) fraction of the total area of the sphere.