Shape of the hot topological charge density spectral function
M. Laine (AEC, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, Bern, CH-3012, Switzerland); L. Niemi (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, 200240, China, Department of Physics and Helsinki Institute of Physics, University of Helsinki, FI-00014, Finland); S. Procacci (AEC, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, Bern, CH-3012, Switzerland); K. Rummukainen (Department of Physics and Helsinki Institute of Physics, University of Helsinki, FI-00014, Finland)
After motivating an interest in the shape of the topological charge density spectral function in hot Yang-Mills theories, we estimate it with the help of thermally averaged classical real-time simulations, for N c = 2, 3. After subtracting a perturbative contribution at large frequencies, we observe a non-trivial shape at small frequencies (a dip rather than a peak), interpolating smoothly towards the sphaleron rate at zero frequency. Possible frequency scales making an appearance in this shape are discussed. Implications for warm axion inflation and reheating, and for imaginary-time lattice measurements of the strong sphaleron rate, are recapitulated.