Gravity and Quantum Fields Reconciled: New Theory Achieves UV Stability

The persistent conflict between quantum field theory and general relativity receives fresh scrutiny in new work led by Latham Boyle, Neil Turok, and Vatsalya Vaibhav, all from the Higgs Centre for Theoretical Physics at the University of Edinburgh. Researchers have long struggled to reconcile the wildly fluctuating spacetime predicted by quantum mechanics with the smooth, predictable universe we observe, a problem stemming from diverging energy calculations in quantum fields. This team investigates whether specific quantum theories can avoid these divergences, identifying a class of models possessing ‘fixed points’ where gravitational interactions remain stable at all energy levels. Their calculations reveal that theories resembling the Standard Model of particle physics, complete with additional scalar fields, exhibit these desirable properties, potentially offering a pathway towards a consistent theory of quantum gravity and a universe with a vanishingly small cosmological constant.

Current approaches often encounter problems at extremely high energies, leading to unpredictable results. This research explores alternative theories designed to remain well-behaved even under these extreme conditions, moving beyond traditional field theories to incorporate more complex mathematical structures. The team investigates higher-derivative field theories, which include terms that consider the rates of change of fields to higher powers. These terms can potentially tame the troublesome divergences that plague standard quantum field theories and offer a more complete description of fundamental physics, potentially providing a pathway toward a consistent quantum theory of gravity.

However, higher-derivative theories present significant challenges, including the potential appearance of particles with negative kinetic energy, known as ghosts, which can lead to instabilities. Even without explicit ghosts, these theories can violate unitarity and causality, making predictions unreliable. The authors explore strategies to overcome these challenges, investigating whether mathematical transformations can eliminate instabilities and whether quantum effects might tame instabilities that appear at the classical level. The team also explores the role of CPT symmetry, a fundamental principle relating charge, parity, and time reversal, in stabilizing the theory and resolving issues with ghosts.

Specific models investigated include scalar field theories with fourth-derivative terms, higher-derivative versions of the Abelian Higgs model, and theories of gravity incorporating higher derivatives, as well as non-local field theories where the action depends on the field at multiple points in spacetime. The results suggest that quantum effects can play a crucial role in stabilizing higher-derivative theories, and that CPT symmetry is important for resolving issues with ghosts, potentially providing a UV-complete description of physics. This research has connections to particle physics, cosmology, and the broader quest for a consistent quantum theory of gravity, representing a deep dive into the theoretical challenges and potential solutions associated with building a UV-complete quantum field theory.

Running Couplings and Quantum Field Effects

Researchers are investigating whether quantum field theories can consistently couple to gravity, addressing a long-standing problem where calculations of gravity often produce infinite results. They employed sophisticated mathematical techniques involving heat kernel methods to calculate how various quantum fields affect gravitational couplings, specifically, the cosmological constant and Newton’s constant, at extremely high energies. This approach traces the behavior of these couplings as energy scales change, revealing whether they converge or diverge. The core of the methodology centers on analyzing the “running” of the gravitational couplings, which describes how their values change with energy.

Scientists calculated the beta functions, equations that govern these changes, for a broad class of quantum field theories, considering contributions from scalar particles, fermions, and gauge bosons. The calculations involved evaluating complex traces using heat kernel expansion, a technique that expresses the trace of a function of a differential operator as an infinite series. The team discovered a specific class of quantum field theories where these divergences cancel out, resulting in finite and well-behaved gravitational couplings. This cancellation occurs when the theory possesses “UV fixed points,” meaning the couplings remain stable at very high energies. Notably, the Standard Model of particle physics does not exhibit this desirable property, leading to divergent behavior. However, the researchers demonstrated that certain modifications to the Standard Model, specifically, including right-handed neutrinos, can bring the theory closer to a consistent coupling with gravity, suggesting that a successful theory of quantum gravity may require a specific balance between different types of quantum fields to ensure the stability of spacetime at the smallest scales.

Well-Behaved Quantum Fields Reconcile with Gravity

This research demonstrates a pathway to reconcile quantum field theory with gravity by identifying specific field configurations that avoid problematic divergences. Scientists investigated whether certain quantum field theories could consistently couple to gravity without generating infinite values in calculations, a long-standing challenge in theoretical physics. The team focused on the behavior of the “stress tensor,” a quantity describing the distribution of energy and momentum, and its impact on spacetime curvature. Experiments revealed that a carefully constructed theory, incorporating both standard particles and “Fradkin-Tseytlin” (FT) scalars, exhibits a unique property: its gravitational interactions remain well-behaved even at extremely high energies.

Specifically, the calculations show that for a theory with specific ratios of particle types, the problematic divergences cancel out, ensuring the theory remains finite and consistent when coupled to gravity. The team’s analysis extends to a model closely resembling the Standard Model of particle physics, incorporating 12 gauge fields and 48 Weyl spinors. Adding 36 FT scalars to this model, while eliminating conventional two-derivative scalars, successfully cancels the leading-order vacuum energy and Weyl anomalies, further stabilizing the theory. Measurements confirm that this configuration maintains a positive Newton’s constant and allows for an arbitrarily small cosmological constant, crucial for describing the observed universe. Furthermore, the research demonstrates that the theory’s gravitational coupling remains constant over time in the infrared limit, suggesting the potential for a consistent quantum theory of gravity based on these principles and opening avenues for exploring the early universe and the nature of spacetime itself.

UV Fixed Points Resolve Quantum Gravity Conflicts

This research investigates whether quantum field theories can be constructed that avoid the problematic divergences typically encountered when combining quantum mechanics with gravity. The team demonstrates the existence of a specific class of quantum field theories, including models resembling the Standard Model of particle physics, possessing ultraviolet (UV) fixed points. These fixed points ensure that certain calculations remain finite even at extremely high energies, resolving a long-standing conflict between quantum theory and general relativity, and aligning with observed cosmological properties. The study builds on previous work exploring higher-derivative gravity and renormalization group flows, identifying conditions under which the troublesome divergences cancel. While the research does not claim to have solved all the challenges of quantum gravity, it provides a concrete example of a theory with improved UV behavior. The authors acknowledge that further investigation is needed to fully understand the implications of these findings, particularly concerning the precise values of fundamental constants and the connection to observable phenomena.