The instanton liquid and the axion
Shellard, E. P. S.
University of Cambridge
Department of Applied Mathematics and Theoretical Physics
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Wantz, O. (2010). The instanton liquid and the axion (doctoral thesis). https://doi.org/10.17863/CAM.16091
Description of the low energy regime of QCD in terms of a self-interacting ensemble of instantons, the instanton liquid, at zero and finite temperature. The application addressed in this thesis is a precise determination of the axion mass, at all temperatures, within this framework.
The ultimate goal of this thesis is to improve our understanding of the cosmology of axions. Axions couple to QCD instantons and these non-perturbative effects are modeled within the framework of the interacting instanton liquid model (IILM). The thesis describes the significant advances made within the IILM in order to study the quark-gluon plasma in realistic parameter regimes. In particular, a determination of the temperature-dependent axion mass in the IILM lays the foundation for a critical reevaluation and update of present cosmological axion constraints. We develop grand canonical Monte Carlo routines to study topological fluctuations in the quark-gluon plasma. The model is calibrated against the topological susceptibility at zero temperature, in the chiral regime of physical quark masses. A numerical framework to derive interactions among the pseudo-particles is developed that is in principle exact, and is used to cure a pathology in the presently available finite temperature interactions. The IILM reduces field theory to a molecular dynamics description, and we show that, quite generically, the dynamics for non-trivial backgrounds in the presence of light quarks is reminiscent of a strongly associating fluid. To deal with the well-known difficulty in simulating ionic fluids, we develop advanced algorithms based on Biased Monte Carlo techniques. We study the IILM at finite temperature in the quenched and unquenched sector, with due diligence to a consistent thermodynamic limit. Of particular interest is chiral symmetry breaking and the temperature dependence of the topological susceptibility, and we study in detail the effects of instanton--anti-instanton pairs. Our determination of the topological susceptibility provides, for the first time, a well-motivated axion mass for all temperatures. The misalignment mechanism for axion production is studied in detail, solving the evolution equations exactly in a radiation dominated FRW universe with the full temperature dependence of the effective degrees of freedom taken into account. Improved constraints in the classic and anthropic axion window are derived. We generalise the latter to large angle fine-tuning by including in the isocurvature contribution to the cosmic microwave background radiation the full anharmonic axion potential effects. Finally, we reexamine bounds from axion string radiation in the thermal scenario to complete a comprehensive update of all cosmological axion constraints.
QCD, Axion, Cosmology, Instanton, Caloron, Instanton Liquid
This record's DOI: https://doi.org/10.17863/CAM.16091