Searching for a $C$-function on the three-dimensional sphere

Abstract

We present a detailed analytic study on the three-dimensional sphere of the most popular candidates for $C$-functions, both for Dirac and scalar free massive fields. We discuss to which extent the effective action, the Rényi entanglement entropy and the renormalized entanglement entropy fulfill the conditions expected from $C$-functions. In view of the absence of a good candidate in the case of the scalar field, we introduce a new candidate, which we call the modified effective action, and analyze its pros and cons.

24 pages, 13 figures

References in corpus (5)

• Towards a derivation of holographic entanglement entropy
• Entanglement entropy for odd spheres
• Renormalization group flow of entanglement entropy on spheres
• Massive sphere determinants
• Topological Entropy and Renormalization Group flow in 3-dimensional spherical spaces

Cited by in corpus (1)

• Holographic RG flows on curved manifolds and the $F$-theorem