Matter Spectral Functions from Quantum Gravity

TL;DR

This paper explores how quantum gravity influences matter spectral functions, demonstrating that gravitational interactions modify both infrared and ultraviolet behaviors, and establishing the spectral representation within an asymptotically safe framework.

Contribution

It provides the first detailed analysis of matter spectral functions coupled to Lorentzian quantum gravity, showing how gravity alters matter propagators and form factors.

Findings

Matter spectral functions possess a K"allén-Lehmann representation.

Gravity modifies the infrared and ultraviolet behavior of matter spectral functions.

The study uses functional renormalisation in Lorentzian signature to achieve results.

Abstract

We investigate Lorentzian quantum gravity coupled to a template matter sector with gauge fields, scalars and fermions. In the absence of quantised gravity, the matter sector by itself is renormalisable, but UV-incomplete. Provided quantum gravity offers an asymptotically safe UV-completion, we determine the photon and scalar two-point functions in the presence of gravitational fluctuations, and show that both possess a K\"all\'en-Lehmann spectral representation. Our results are achieved using functional renormalisation adapted for theories in Lorentzian signature. We explain why and how interactions with gravity modify both the infrared as well as the ultraviolet behaviour of matter spectral functions. We further determine the corresponding form factors on the level of the quantum effective action. Limitations and extensions of our study are discussed alongside implications for particle physics and unitarity of quantum gravity with matter.