Sphere Renyi entropies

Abstract

I give some scalar field theory calculations on a d-dimensional lune of arbitrary angle, evaluating, numerically, the effective action which is expressed as a simple quadrature, for conformal coupling. Using this, the entanglement and Renyi entropies are computed. Massive fields are also considered and a renormalisation to make the (one-loop) effective action vanish for infinite mass is suggested and used, not entirely successfully. However a universal coefficient is derived from the large mass expansion. From the deformation of the corresponding lune result, I conjecture that the effective action on all manifolds with a simple conical singularity has an extremum when the singularity disappears. For the round sphere, I show how to convert the quadrature form of the conformal Laplacian determinant into the more usual sum of Riemann zeta functions (and log2).

15 pages, 6 figures. Conjecture on extremum of effective action on conically deformed manifolds made. References added

References in corpus (5)

• Seeing a c-theorem with holography
• Entanglement Entropy in the O(N) model
• Some Calculable Contributions to Entanglement Entropy
• Entanglement Entropy in Scalar Field Theory
• Determinants and conformal anomalies of GJMS operators on spheres

Cited by in corpus (10)

• A universal feature of CFT Renyi entropy
• Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories
• Free energy and defect $C$-theorem in free scalar theory
• Renormalization group flow of entanglement entropy on spheres
• Supersymmetric Renyi Entropy and Weyl Anomalies in Six-Dimensional (2,0) Theories
• On Renyi entropy for free conformal fields: holographic and q-analog recipes
• Lens space determinants
• Information Theoretic Inequalities as Bounds in Superconformal Field Theory
• Searching for a $C$-function on the three-dimensional sphere
• Quantum Field Theory on spherical space forms