The boundary F-theorem for free fields

TL;DR

This paper investigates the boundary free energy for free fields on hemispheres and lunes, establishing its equivalence to determinants and free energies for scalars and spin-half fields across arbitrary dimensions.

Contribution

It demonstrates the equivalence of boundary free energy with N-D determinants and spin-half free energies, extending results to arbitrary dimensions and different geometries.

Findings

Boundary free energy equals N-D determinant for free scalars.

Boundary free energy matches spin-half free energy up to spin degeneracy.

Results hold for hemispheres and lunes in any dimension.

Abstract

The boundary free energy, as defined by Gaiotto, is further analysed for free scalars on a hemisphere and shown to be the same as the N-D determinant that earlier occurred in a treatment of GJMS operators. It is also shown to be identical, up to spin degeneracy, to the free energy for a spin-half field on the hemisphere boundary. This is also true if the hemisphere is replaced by a lune. The calculations are carried out in arbitrary dimensions.