Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry

Understand

In this work, we consider a noncommutative (NC) massless scalar field coupled to the classical nonrotational BTZ geometry.

• In a manner of the theories where the gravity emerges from the underlying scalar field theory, we study the effective action and the entropy derived from this noncommutative model.
• In particular, the entropy is calculated by making use of the two different approaches, the brick wall method and the heat kernel method designed for spaces with conical singularity.
• We show that the UV divergent structures of the entropy, obtained through these two different methods, agree with each other.