Fixed points of classical gravity coupled with a Standard-Model-like theory

Abstract

Coupling quantum field theory (QFT) \!-\! even free QFT \!-\! to gravity leads to well-known problems. In particular, the stress tensor $T_{\hat{I}¼\hat{I}½}$ (gravity's source) and its correlators typically diverge in the UV, creating a conflict between the wildly inhomogeneous spacetime we expect quantum mechanically and the weakly-curved, macroscopic spacetime we observe. Are there QFTs for which these divergences cancel? Here, for simplicity, we consider free quantum fields on a classical curved background. The aforementioned divergences are related to the running of the gravitational couplings. We calculate the corresponding beta functions, identifying a special class of QFTs with UV fixed points at which $⟨T_{\hat{I}¼\hat{I}½}⟩$ and all its correlators $⟨T\dots T⟩$ are UV finite. An intriguing example is a theory like the Standard Model (including right-handed neutrinos) with $12$ gauge fields, $3$ generations of $16$ Weyl fermions and $36$ four-derivative (Fradkin-Tseytlin) scalars. In the infrared, this theory has a positive Newton's constant $G$ and an arbitrarily small cosmological constant $\hat{I}›$.

7 pages, 1 figure