On $a$-$F$ dimensional interpolation

TL;DR

This paper derives a new dimensional interpolation between free energy and conformal anomaly for scalar and spinor fields on spheres, connecting field theory and AdS/CFT results with potential implications for higher derivative theories.

Contribution

It introduces a novel interpolation method extending previous work, linking free energy and conformal anomaly, and explores higher derivative extensions with insights into non-minimal Type-B mismatch.

Findings

Derived a simple integral for the interpolation between free energy and anomaly.

Connected the interpolation to AdS/CFT results by Giombi and Klebanov.

Extended the approach to GJMS-type higher derivatives.

Abstract

A dimensional interpolation between the free energy and conformal anomaly on spheres is derived for free scalar and spinor fields on the basis of standard field theory. The regularisation used is an extension of one by Candelas and Weinberg. It yields a (known) simple integral which is shown to be identical to the interpolations introduced by Giombi and Klebanov using earlier AdS/CFT results. The extension to GJMS--type higher derivatives is made with a hint of a possible, kinematic resolution of the non--minimal Type-B mismatch being presented. Another form of the sphere conformal anomaly is given.