Quantum Gravity Calculations Reveal Leading Order Dimension 6 Operators

The fundamental nature of gravity at extremely high energies remains one of the most challenging problems in theoretical physics, and understanding its quantum properties is crucial for a complete description of the universe. Tommaso Antonelli, Xavier Calmet, and Stephen D. H. Hsu, researchers at the University of Sussex and Michigan State University, investigate the quantum effects of gravity by calculating how gravitons, the hypothetical particles mediating gravitational force, interact with other particles. Their work reveals that the leading order effects of these interactions produce non-local operators with dimension six, meaning gravity’s quantum effects manifest in ways that connect distant points in spacetime, and importantly, that simpler, dimension five operators do not arise from standard perturbative calculations. This discovery has significant implications for theoretical models attempting to explain dark matter, particularly those involving ultralight scalar particles, and provides new insights into the structure of quantum gravity itself.

Dimension 5 operators are not generated by perturbative, or weak field, effects, although they might be generated by strong field effects such as Planck-scale fluctuations in spacetime. We investigate the consequences of our findings for models of ultralight scalar dark matter.

Graviton Exchange and Effective Action Calculation

This research explores the effective action arising from graviton exchange and its implications for physics beyond the Standard Model. The calculations focus on determining how gravitons, the quantum particles mediating gravity, influence other fields by integrating out high-energy degrees of freedom. Graviton exchange can lead to interactions even if particles don’t directly interact through known forces. Calculations are performed by expanding the metric around flat spacetime, a standard technique in quantum field theory and general relativity, and utilizing the de Donder gauge to simplify calculations and ensure consistency.

The stress-energy tensor, describing energy and momentum distribution, plays a central role in determining graviton-mediated interactions, with a focus on non-minimal couplings between gravity and other fields. The calculations reveal that the effective action is non-local, meaning interactions between particles depend on the history of the fields, a common feature of theories involving gravity. The non-minimal coupling between gravity and scalar fields leads to a local contribution to the effective action, simplifying calculations and potentially revealing observable effects. These findings have implications for areas including dark matter, axions, modified gravity, and precision tests of gravity. This work provides a rigorous theoretical framework for understanding graviton exchange and has potential applications in various phenomenological studies. The results highlight the importance of experiments probing the non-local nature of gravity and searching for interactions mediated by gravitons, such as those using atomic clocks and interferometers.

Gravitational Interactions Avoid Linear Dark Sector Coupling

Scientists have demonstrated that calculations involving gravity’s influence on matter fields do not generate dimension five operators, even at the one-loop level. This establishes a key result regarding the nature of interactions between visible and hidden sectors of the universe. The research team calculated effective operators arising from graviton exchange between standard model fields and those of a hidden sector, revealing that the leading order operators are non-local and of dimension six. These calculations, performed at both tree-level and one-loop order, confirm that the gravitationally generated interaction is always quadratic in the dark field. The team’s calculations show that the effective action takes the form of an integral over spacetime, involving the stress-energy tensor and the graviton propagator, ultimately leading to the dimension six operators. The research team investigated the implications of these findings for models of ultralight scalar dark matter, recovering interactions consistent with previously discussed local dimension six operators.

Higher-Dimensional Operators From Graviton Exchange

This work investigates the generation of higher-dimensional operators through graviton exchange, examining interactions between standard model particles and those of a hypothetical hidden sector. Calculations demonstrate that, at tree level, the leading operators generated are non-local and of dimension six, while one-loop effects produce dimension eight operators. These findings challenge the expectation that perturbative quantum gravity will generate dimension five operators connecting all fields. The research establishes that, within the framework of perturbative quantum gravity, symmetry-breaking effects on the tree-level action do not arise from the generation of these higher-dimensional operators. Future research directions include exploring the implications of these findings for models incorporating ultralight scalar dark matter and investigating the behaviour of the system beyond the perturbative approximation. These results refine our understanding of how gravity connects different sectors of particle physics and provide a more nuanced picture of quantum gravitational effects.