Entanglement entropy on a fuzzy sphere with a UV cutoff

Understand

We introduce a UV cutoff into free scalar field theory on the noncommutative (fuzzy) two-sphere.

• Due to the IR-UV connection, varying the UV cutoff allows us to control the effective nonlocality scale of the theory.
• In the resulting fuzzy geometry, we establish which degrees of freedom lie within a specific geometric subregion and compute the associated vacuum entanglement entropy.
• Entanglement entropy for regions smaller than the effective nonlocality scale is extensive, while entanglement entropy for regions larger than the effective nonlocality scale follows the area law.