Shape of the hot topological charge density spectral function

TL;DR

This paper investigates the spectral function of topological charge density in hot Yang-Mills theories using classical real-time simulations, revealing a non-trivial shape at low frequencies with implications for cosmology and lattice measurements.

Contribution

It provides the first non-perturbative estimate of the spectral function shape at small frequencies in hot Yang-Mills theories for different N_c, highlighting a dip instead of a peak.

Findings

Spectral function exhibits a dip at low frequencies.

Interpolates smoothly to the sphaleron rate at zero frequency.

Discusses implications for axion inflation and lattice measurements.

Abstract

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 $N_{\rm c} = 2,3$. 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.