Bootstrapping the Chiral-Gravitational Anomaly: Constraints on Theories with Axions and Higher-Spin Resonances from Causality and Unitarity

Concepts de base

The chiral-gravitational anomaly imposes bounds on the mass scale of higher-spin resonances in theories with axions or strongly-coupled gauge theories, potentially impacting our understanding of quantum gravity and beyond-Standard Model physics.

Résumé

• Bibliographic Information: Dong, Z.-Y., Ma, T., Pomarol, A., & Sciotti, F. (2024). Bootstrapping the Chiral-Gravitational Anomaly. arXiv:2411.14422v1 [hep-th].
• Research Objective: This paper investigates the constraints imposed by causality and unitarity on theories with U(1)-gravitational anomalies, aiming to establish new bounds on the mass scale of higher-spin resonances in such theories.
• Methodology: The authors employ bootstrap techniques, analyzing the analyticity, positivity, and crossing symmetry of graviton scattering amplitudes in the presence of a U(1)-gravitational anomaly. They utilize dispersion relations and smearing techniques to derive rigorous bounds on the mass scale of higher-spin states.
• Key Findings: The study reveals a universal scale (Λcaus), dictated by the anomaly coefficient, at which states with spin J ≥ 4 must appear in theories with U(1)-gravitational anomalies. This scale can be lower than the Planck scale, particularly in axion models where Λcaus ∼ √(MP * fa), with fa being the axion decay constant. In strongly-coupled gauge theories, glueballs can evade these bounds under specific conditions. However, in holographic 5D models, Λcaus emerges as a new cutoff scale unless certain conditions on the 5D parameters are met.
• Main Conclusions: The research demonstrates that the chiral-gravitational anomaly has significant implications for the consistency of theories with axions and higher-spin resonances. The derived bounds impose new constraints on the allowed parameter space of such models and suggest the existence of new physics beyond the Standard Model at scales potentially accessible to future experiments.
• Significance: This work contributes significantly to our understanding of quantum gravity and beyond-Standard Model physics by highlighting the interplay between anomalies, causality, and the emergence of new particles. The findings have profound implications for model building in these areas and provide new avenues for exploring the fundamental nature of gravity and particle physics.
• Limitations and Future Research: The analysis primarily focuses on 2 → 2 scattering amplitudes and assumes specific high-energy behaviors. Further research could explore higher-point amplitudes and alternative high-energy completions. Additionally, investigating the phenomenological consequences of these bounds for specific axion models and their potential experimental signatures would be of great interest.

Stats

κg = Nc/192π^2 for one-flavor QCD.
For axion models, Fπ/κg ∼ fa, where fa is the axion decay constant.

Citations

"Here we would like to extend the analysis of [18] to theories with U(1)-gravitational anomalies."
"Our main motivation is to obtain information on possible models of higher-spin resonances that in the IR contain a coupling of η to two gravitons."
"These are models dual to gauge theories in the large 't Hooft coupling."

Idées clés tirées de

Bootstrapping the Chiral-Gravitational Anomaly

by Zi-Yu Dong, ... à arxiv.org 11-22-2024

https://arxiv.org/pdf/2411.14422.pdf

Questions plus approfondies

How do these findings concerning the chiral-gravitational anomaly potentially influence the search for dark matter candidates, particularly those proposed within the framework of axion-like particles?

The findings presented in the paper have significant implications for the search for dark matter in the form of axion-like particles (ALPs). Here's how:

Constraining ALP Models: The paper derives a new cutoff scale, Λcaus, for axion-like EFTs due to the chiral-gravitational anomaly. This scale, given by Λcaus ~ √(MPfa), where MP is the Planck mass and fa the axion decay constant, dictates the energy scale below which new states beyond the axion must appear. This has direct consequences for model building:

Ultra-light Axions: Models proposing ultra-light axions with very large fa (to address issues like the strong CP problem) are pushed towards even higher fa to keep Λcaus above the relevant energy scales for dark matter interactions.
New Particles and Interactions: The existence of Λcaus implies that ALP models cannot be complete without considering additional particles and interactions beyond the simple axion-photon coupling often used in experimental searches. This could involve heavier ALPs, new gauge bosons, or other exotic particles.

Experimental Implications:

Direct Detection: The presence of new states below Λcaus could open up new channels for direct detection experiments. For example, if heavier ALPs exist, they might be accessible in experiments designed for higher mass ranges.
Indirect Detection: The new particles and interactions could also lead to novel indirect detection signatures, such as unique decay channels or annihilation products that could be searched for in astrophysical observations.

Theoretical Landscape: The findings emphasize the importance of considering quantum gravity effects, even at low energies, when studying axion-like dark matter. This could motivate further theoretical investigations into the interplay between axions, gravity, and UV completions of the Standard Model.
In summary, the paper's results highlight the limitations of simple ALP EFTs and encourage a more comprehensive approach to axion dark matter model building and experimental searches. The presence of Λcaus suggests a richer phenomenology than previously considered, potentially offering new avenues for discovery.

Could the presence of a low cutoff scale, as dictated by the chiral-gravitational anomaly, be interpreted as evidence against certain string theory compactifications or other high-energy completions of quantum gravity?

The presence of a low cutoff scale, Λcaus, arising from the chiral-gravitational anomaly does not necessarily rule out string theory compactifications or other high-energy completions of quantum gravity. However, it does impose constraints on the types of low-energy effective field theories (LEFTs) that can be consistently embedded within such frameworks. Here's why:

String Theory and EFTs: String theory compactifications typically give rise to a plethora of light states in the low-energy spectrum, including scalar fields (moduli), gauge bosons, and fermions. These states can contribute to the chiral-gravitational anomaly and modify the value of Λcaus.
Constraints on Compactifications: The bound on Λcaus implies that certain string compactifications leading to LEFTs with a large chiral-gravitational anomaly and no new states below Λcaus would be inconsistent. This is because the presence of the anomaly necessitates the existence of new physics below that scale to ensure unitarity and causality.
Model Building Implications: Model builders working with string theory compactifications need to carefully consider the low-energy spectrum and the contributions to the chiral-gravitational anomaly. The bound on Λcaus provides a valuable tool to assess the viability of different compactification scenarios and guide the search for realistic models.
Alternative Interpretations: It's important to note that the low cutoff scale could also point towards alternative interpretations:

Strong Coupling: Instead of new weakly coupled states, the low cutoff might indicate the emergence of strong coupling effects below Λcaus. This could signal the breakdown of the perturbative description and the need for non-perturbative methods to study the physics at those energies.
Intermediate Scale Physics: The low cutoff could be a hint of new physics at an intermediate scale between the electroweak scale and the Planck scale. This intermediate scale physics could be related to grand unification, supersymmetry breaking, or other beyond-the-Standard Model scenarios.
In conclusion, while the low cutoff scale from the chiral-gravitational anomaly doesn't directly contradict string theory or other high-energy completions, it does impose non-trivial constraints on the allowed low-energy physics. This highlights the importance of carefully analyzing the low-energy implications of UV complete theories and using consistency conditions like those derived from causality and unitarity to guide model building efforts.

If we consider the universe as a holographic projection from a higher-dimensional space, how might the constraints imposed by the chiral-gravitational anomaly manifest themselves in the dynamics of cosmological evolution or the formation of large-scale structures?

The constraints imposed by the chiral-gravitational anomaly, particularly the presence of a low cutoff scale Λcaus, could have intriguing implications for cosmology within the framework of the holographic principle. Here are some speculative possibilities:

Modified Gravitational Dynamics: In holographic cosmology, the dynamics of the universe are encoded in the evolution of a dual quantum field theory residing on a lower-dimensional boundary. The presence of Λcaus in the LEFT could manifest as modified gravitational dynamics at early times or on cosmological scales. This could affect:

Inflation: The inflationary epoch, believed to be responsible for the homogeneity and isotropy of the universe, could be influenced by the modified gravity. This might lead to observable signatures in the cosmic microwave background radiation, such as deviations from the standard inflationary predictions for the spectral index or tensor-to-scalar ratio.
Dark Energy: The late-time accelerated expansion of the universe, attributed to dark energy, could also be connected to the holographic dual and the presence of Λcaus. This might provide new insights into the nature of dark energy and its relationship to fundamental physics.

Large-Scale Structure Formation: The growth of cosmic structures, from galaxies to galaxy clusters, is governed by gravity. Modifications to gravity due to the holographic dual and Λcaus could alter the clustering of matter and leave imprints on the distribution of galaxies and other large-scale structures. This could be probed using galaxy surveys and other cosmological observations.
Black Hole Physics: The holographic principle is deeply connected to black hole physics. The presence of Λcaus might have implications for the thermodynamics and information paradox associated with black holes. It could also influence the formation and evolution of primordial black holes, which are thought to have formed in the early universe.
Connection to Quantum Information: The holographic principle suggests a deep connection between gravity and quantum information. The constraints from the chiral-gravitational anomaly could provide hints about the nature of this connection and the role of quantum information in the emergence of spacetime and gravity.
It's important to emphasize that these are highly speculative ideas, and exploring them rigorously would require a deeper understanding of the holographic duality and its implications for cosmology. Nevertheless, the possibility that low-energy constraints from the chiral-gravitational anomaly could leave observable imprints on the cosmos through the holographic principle is an exciting avenue for future research.