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

Area of Science:

• Theoretical physics
• Quantum gravity
• High-energy physics

Background:

• Evanescent operators (e.g., Gauss-Bonnet term) have zero perturbative matrix elements in D=4.
• Evanescent fields, like three-form fields, do not propagate in D=4.
• These phenomena are dual to cosmological constant contributions.

Purpose of the Study:

• Investigate the impact of evanescent operators and fields on ultraviolet (UV) divergence in pure gravity.
• Analyze the two-loop identical-helicity four-graviton amplitude.
• Examine how p-form duality transformations affect trace anomalies and UV divergences.

Main Methods:

• Computation of the two-loop identical-helicity four-graviton amplitude.
• Determination of the coefficient for the R³ counterterm.
• Comparison of dual theories: gravity with no matter vs. three-form matter, and gravity with zero-form vs. two-form matter.

Main Results:

• Evanescent operators and fields modify the leading UV divergence in pure gravity.
• The leading R³ divergence changes under p-form duality transformations.
• The one-loop trace anomaly (Gauss-Bonnet operator coefficient) also changes under duality transformations.

Conclusions:

• Despite changes in divergence under duality, physical renormalized amplitudes can be chosen to respect duality.
• The renormalization-scale dependence of the physical amplitude remains unaltered by duality transformations.
• This work clarifies the role of evanescent phenomena in quantum gravity divergences and duality symmetries.