In this article we investigate aspects of entanglement entropy and mutual
information in a large-N strongly coupled noncommutative gauge theory, both at
zero and at finite temperature. Using the gauge-gravity duality and the
Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial
regions on such noncommutative geometries and subsequently compute the
corresponding entanglement entropy. We observe that for regions which do not
lie entirely in the noncommutative plane, the RT-prescription yields sensible
results. In order to make sense of the divergence structure of the
corresponding entanglement entropy, it is essential to introduce an additional
cut-off in the theory. For regions which lie entirely in the noncommutative
plane, the corresponding minimal area surfaces can only be defined at this
cut-off and they have distinctly peculiar properties.Comment: 28 pages, multiple figures; minor changes, conclusions unchange