An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse (1004.5138v2)

Abstract: We give an explicit realization of the "String Axiverse" discussed in Arvanitaki et. al \cite{Arvanitaki:2009fg} by extending our previous results on moduli stabilization in $M$ theory to include axions. We extend the analysis of \cite{Arvanitaki:2009fg} to allow for high scale inflation that leads to a moduli dominated pre-BBN Universe. We demonstrate that an axion which solves the strong-CP problem naturally arises and that both the axion decay constants and GUT scale can consistently be around $2\times 10^{16}$ GeV with a much smaller fine tuning than is usually expected. Constraints on the Axiverse from cosmological observations, namely isocurvature perturbations and tensor modes are described. Extending work of Fox et. al \cite{Fox:2004kb}, we note that {\it the observation of tensor modes at Planck will falsify the Axiverse completely.} Finally we note that Axiverse models whose lightest axion has mass of order $10^{-15}$ eV and with decay constants of order $5\times 10^{14}$ GeV require no (anthropic) fine-tuning, though standard unification at $10^{16}$ GeV is difficult to accommodate.

• The paper presents an M theory model that integrates numerous axions to dynamically resolve the strong CP problem.
• It extends moduli stabilization techniques to realize an axiverse, predicting an exponential axion mass spectrum from 10⁻³³ eV to 1 eV.
• Cosmological scenarios outlined in the study offer testable predictions via tensor modes, isocurvature perturbations, and gravitational wave observations.

An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse

The paper by Acharya et al. addresses the strong CP problem within the framework of M theory, proposing a model that aims to solve it through the inclusion of axions from string theory—the so-called "String Axiverse"—which offers intriguing possibilities for high-energy physics and cosmology. By extending previous results on moduli stabilization in M theory to include axions, they provide an explicit realization of this axiverse and explore cosmological constraints and implications.

Key Points and Results

• Strong CP Problem and QCD Axion: The strong CP problem is the question of why the QCD θ-angle is tightly constrained by observation to be extremely small. The Peccei-Quinn mechanism introduces the QCD axion, which dynamically cancels the θ-angle via the axion field.
• Axiverse Realization and Moduli Stabilization: The authors extend moduli stabilization in M theory to incorporate axions as zero modes of antisymmetric tensor fields in extra dimensions. This yields a model wherein hundreds to thousands of axions can be present, characterized by discrete UV boundary conditions, which reflects the topology of the extra dimensions.
• Mass Spectrum and Constraints: Axion masses are predicted to be distributed exponentially across many orders of magnitude, ranging from sub-eV values to GUT scale parameters. This distribution could span from approximately $10^{-33}$ eV to 1 eV, analogous to hierarchy seen in Yukawa couplings in M theory. The authors emphasize that observations of tensor modes can falsify the axiverse scenario entirely, depending on the scale of inflationary Hubble parameters relative to moduli masses.
• Inflationary Scenarios: Two cosmological scenarios are explored: a "non-thermal" moduli dominated pre-BBN universe and a "thermal" cosmology with a radiation-dominated phase. The paper argues that the non-thermal scenario, potentially more generic in string frameworks, allows for larger axion decay constants and less anthropic fine-tuning due to additional entropy production from moduli decay.

Implications and Future Directions

The realization of the axiverse within M theory offers a tantalizing possibility for addressing longstanding issues in both particle physics and cosmology. The alignment of axion decay constants near the GUT scale presents an intriguing intersection with string theory predictions and observable astrophysical phenomena. The model presents natural tests through cosmological signatures, including measurements of isocurvature perturbations, tensor modes, and astrophysical consequences like the spectrum of gravitational waves from axion-black hole interactions.

Moreover, the paper highlights the rich phenomenological implications of having a plethora of ultralight axion-like particles. The range of axion masses predicted by the axiverse suggests potential signals in forthcoming experiments and observations such as the polarization of the CMB, gravitational wave studies, and small scale structure formation—all probes that could substantiate or dismiss the theoretical framework laid out.

Conclusion

This research contributes a detailed theoretical backdrop for solving the strong CP problem and investigating axionic fields from string theory. The interplay between M theory and cosmological observations envisions a path forward to discover such exotic particles and syncretize a comprehensive understanding of the universe at fundamental scales. Future studies could further enlighten the properties and detectability of axions within this framework, thus continuing a profound inquiry into the dynamics of particle physics and the unfolding cosmos.