Asymptotic safety meets tensor field theory: towards a new class of gravity-matter systems (2501.10307v1)

Abstract: Combining asymptotically safe quantum gravity with a tensor field theory, we exhibit the first example of a theory with gravity and scalar fields in four dimensions which may realize asymptotic safety at a non-vanishing value of the scalar quartic coupling. We first present (further) evidence that in the asymptotic-safety paradigm, quantum fluctuations of gravity generically screen the quartic couplings in (multi-)scalar models. For a tensor field theory in which the scalar field transforms under an internal $O(N)^3$ symmetry, this has the effect of replacing asymptotic freedom, recently discovered at large $N$ on a fixed flat background, by an interacting fixed point in the presence of quantum gravity. The fixed point originates from the competition between the effects of the matter self-interactions which, contrary to the usual scalar models, are antiscreening, and the screening gravitational effects.

• The paper demonstrates that asymptotic safety integrated with tensor field theory yields a UV fixed point for gravity-matter systems.
• It employs an O(N)^3 tensor model in the large-N limit to balance gravitational anti-screening against scalar self-interactions.
• The results introduce a promising framework for reconciling high-energy quantum gravity with nontrivial matter couplings in realistic models.

Insights into Asymptotic Safety with Tensor Field Theory

The paper "Asymptotic safety meets tensor field theory: towards a new class of gravity-matter systems" by Astrid Eichhorn, Razvan Gurau, and Zois Gyftopoulos investigates the intriguing possibility of realizing asymptotic safety in quantum gravity coupled with scalar fields in four dimensions. This endeavor is pursued by combining the paradigm of asymptotically safe quantum gravity with tensor field theories.

Asymptotic Safety and Quantum Gravity

Asymptotic safety relies on a non-trivial fixed point of the renormalization group (RG) flow, which affords ultraviolet (UV) completeness to a theory. This scenario is particularly compelling for quantum gravity, where traditional methods face challenges due to the non-renormalizable nature of gravity in four dimensions. By positing that the gravitational couplings approach an interacting fixed point in the UV, asymptotic safety could render gravity predictive at high energies.

Incorporating matter into the framework of asymptotic safety necessitates careful consideration of gravitational effects on the beta functions of matter couplings. Historically, gravitational contributions have been seen to "screen" scalar self-interactions, effectively lowering the scale at which a Landau pole might appear in models without additional stabilizing interactions.

Tensor Field Theories

Tensor field theories introduce an innovative approach by employing fields indexed by multiple indices, transforming under product symmetries such as $O(N)^3$. These theories present a novel large-N expansion that reveals intriguing properties distinct from conventional field theories. Notably, some tensor models can exhibit asymptotic freedom with imaginary coupling constants, offering a fresh perspective on UV behavior.

In this work, the authors extend the intriguing properties of tensor field theories to the field of quantum gravity. They specifically explore an $O(N)^3$ tensor model in conjunction with gravity, scrutinizing the interplay between gravitational and tensor field fluctuations.

Large-N Limit and Gravitational Contributions

The paper reveals that, in the large-N limit, tensor field interactions can lead to a delicate balance between anti-screening self-interactions and gravitational screening. Remarkably, this balance allows for the existence of a UV interacting fixed point with non-zero quartic scalar couplings. Here, the impact of gravity no longer necessarily demands the vanishing of scalar self-interactions. Such a configuration challenges prior findings where scalar interactions effectively disappeared via gravitational screening alone.

Critical to their analysis is the behavior of gravitational fixed points under the influence of a large number of scalar fields. The authors assume that the dominant gravitational contribution to the beta functions remains substantial even at large N, implying that quantum gravity continues to influence matter sector couplings significantly.

Implications and Future Prospects

This paper introduces novel possibilities for constructing UV-complete models of gravity coupled to matter with richer interaction structures. The existence of non-trivial fixed points for gravity-matter systems implies a path toward reconciling scalar fields and gravitational interactions in high-energy physics. Additionally, the results bear significant implications for phenomenological models such as hidden sector theories that could engage with scalar-tensor frameworks.

The exploration of coupling non-unitary tensor models, their beta functions, and stability criteria opens new venues for researching beyond-Standard-Model physics and cosmology — particularly where scalar fields play a pivotal role.

Future avenues will likely involve extending these findings to finite cases of N, exploring phenomenological ramifications, or refining the gauge and truncation-related aspects of the functional renormalization group approach to enhance the robustness and applicability of these asymptotically safe models.

Through this integrative approach of tensor field theories and quantum gravity, the authors provide compelling insights that contribute to the evolving understanding of gravity-matter interactions under asymptotic safety, while setting a fertile ground for further explorations into the microscopic structure of quantum space-time.