Asymptotic safety in higher-derivative gravity (0901.2984v2)

Abstract: We study the non-perturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The non-perturbative contributions to the $\beta$-functions shift the known perturbative ultraviolet fixed point into a non-trivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

• The paper demonstrates the existence of a non-Gaussian fixed point with three UV-attractive directions in higher-derivative gravity.
• The authors apply functional renormalization group techniques to non-perturbatively compute β-functions, refining previous perturbative methods.
• The study suggests that quantum effects can mitigate unitarity issues, offering a promising route to a predictive and consistent quantum gravity theory.

Asymptotic Safety in Higher-Derivative Gravity

The paper "Asymptotic Safety in Higher-Derivative Gravity" by Benedetti, Machado, and Saueressig explores the renormalization group flow within the framework of higher-derivative gravity. This paper leverages functional renormalization group techniques, addressing challenges associated with the non-perturbative renormalization of gravity theories extended by higher-order derivative terms.

Core Contributions and Results

The authors establish the existence of a non-Gaussian fixed point (NGFP) in the renormalization group flow of a higher-derivative gravity model. This fixed point distinguishes itself by having three UV-attractive eigendirections and one UV-repulsive direction. Such a configuration aligns with the asymptotic safety conjecture proposed by Weinberg, suggesting that gravity could be made predictive and free from divergences at highly energetic scales.

The critical analysis extends past perturbative approaches, traditionally hampered by unitarity issues originating from so-called "poltergeist" states in higher-derivative theories. The inclusion of the Weyl-squared and other fourth-order derivative terms in their action potentially mitigates these concerns through quantum effects induced by the NGFP. Numerical estimates provide the fixed point values: $g_0^* = 0.00442$, $g_1^* = -0.0101$, $g_2^* = 0.00754$, and $g_3^* = -0.0050$. The stability coefficients further solidify the fixed point's role in the asymptotic safety framework, demonstrating real values that denote the RG flow behavior in the vicinity of the NGFP.

Methodological Insights

The approach utilizes the effective average action and functional renormalization group equations (FRGE) to investigate the quantum effects of higher-derivative operators. The authors adopt a truncation method in their calculation, computing non-perturbative $\beta$-functions by resolving the FRGE for a selected slice of the gravitational $\Gamma_k$ action. The inclusion of higher-derivative terms such as $C^2$ enriches their approximation, providing data not captured in prior studies constrained to simpler $f(R)$ frameworks.

Implications and Future Directions

The implications of this work are profound, both theoretically and practically. By establishing an NGFP with the discussed properties, the paper suggests a viable pathway to resolving the troubling issues of non-unitarity without discarding the benefits of improved UV behaviors inherent in higher-derivative formulisms. The mechanism by which poltergeists might be eliminated implies a potentially unitary asymptotically safe quantum gravity, offering a fresh perspective on the consistency of higher-derivative theories.

Moving forward, this research indicates several avenues for deeper exploration. Expanding the truncation to incorporate even more extensive classes of curvature terms could refine the accuracy of the fixed point estimates. Coupled with advanced computational techniques, such investigations might one day culminate in rigorous proofs of asymptotic safety within quantum gravity.

This paper not only complements existing literature on quantum gravity but also sets a foundation for future theoretical advancements. The nuances in their approach to asymptotic safety contribute significantly to the theoretical toolkit available to researchers venturing into quantum gravitational phenomena.

In summary, "Asymptotic Safety in Higher-Derivative Gravity" provides a meticulous examination of the intricacies of quantum gravity under the auspices of higher-derivative interactions, making substantial strides towards a consistent, unitary, and predictive framework.