Entanglement entropy for odd spheres

TL;DR

This paper explores the relationship between effective action on odd spheres and entanglement entropy, showing that the derivative of the effective action vanishes at q=1, linking it to entanglement entropy.

Contribution

It provides a non-rigorous demonstration that the effective action on odd spheres relates directly to entanglement entropy, with specific numerical examples.

Findings

Effective action derivative vanishes at q=1 for odd spheres.

Effective action equals negative entanglement entropy for a (d-2)-sphere.

Numerical values supporting the theoretical relationship.

Abstract

It is shown, non--rigorously, that the effective action on a Z_q factored odd spheres (lune) has a vanishing derivative at q=1. This leaves the effective action on the ordinary odd d-sphere as (minus) the value of the entanglement entropy associated with a (d-2)-sphere. Some numbers are given.