Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences

TL;DR

This paper investigates how evanescent operators and fields influence the ultraviolet divergences in quantum gravity, revealing that while divergences change under duality transformations, physical amplitudes remain unaffected.

Contribution

It demonstrates that evanescent operators and fields modify the leading UV divergence in pure gravity and explores the impact of duality transformations on these divergences and physical amplitudes.

Findings

Evanescent operators alter the leading UV divergence in gravity.

Duality transformations change the divergence coefficients.

Physical amplitudes can be chosen to respect duality, keeping their scale dependence unchanged.

Abstract

Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D=4 dimensions. Similarly, evanescent fields do not propagate in D=4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (non-evanescent) R^3 counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D=4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop conformal anomaly --- the coefficient of the Gauss-Bonnet operator --- changes under p-form duality transformations. We concur, and also find that the leading R^3 divergence changes under duality transformations. Nevertheless, in both cases the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.