Entanglement Entropy and Matter-Gravity Couplings for Fuzzy Geometry

TL;DR

This paper explores how entanglement entropy in fuzzy geometry depends on background fields and spin connection, linking it to Chern-Simons forms and thermodynamic gravity, and examines matter-gravity couplings with nonminimal curvature terms.

Contribution

It introduces a framework connecting entanglement entropy in fuzzy geometry with generalized Chern-Simons forms and analyzes matter-gravity couplings with specific nonminimal curvature interactions.

Findings

Entanglement entropy relates to generalized Chern-Simons forms.

Matter-gravity couplings induce nonminimal curvature terms.

Framework links fuzzy geometry, thermodynamics, and gravity.

Abstract

In this talk I discuss some features of the entanglement entropy for fuzzy geometry, focusing on its dependence on the background fields and the spin connection of the emergent continuous manifold in a large $N$ limit. Using the Landau-Hall paradigm for fuzzy geometry, this is argued to be given by a generalized Chern-Simons form, making a point of connection with the thermodynamic view of gravity. Matter-gravity couplings are also considered in the same framework; they naturally lead to certain specific nonminimal couplings involving powers of the curvature.