From strong interactions to Dark Matter: the non-perturbative QCD sphaleron rate

Abstract

Acceptance plenary talk for the 2025 Kenneth G.~Wilson Award for Excellence in Lattice Field Theory: For significant contributions to the understanding of topology in QCD, QCD-like, and large-$N_c$ gauge theories, including algorithmic developments to reduce topological freezing, studies of Dirac spectral properties, and axion phenomenology.

Figures (7)

• Figure 1: Semiclassical cartoon of the landscape of topologically-non-equivalent Yang--Mills vacua, labeled by an integer winding number $n$, and of a sphaleron transition above the potential barrier.
• Figure 2: Cartoon representing the Chiral Magnetic Effect in the presence of a sphaleron-induced quark chiral imbalance.
• Figure 3: Left panel: example of the calculation of the sphaleron rate from the inverse problem resolution via the HLT method. Right panel: comparison between the reconstructed smearing kernel $\Delta(\omega)$ for $\lambda=\lambda_1$ and the chosen target one $\delta_\sigma(\omega)$. Figures from Ref. Bonanno:2023ljc.
• Figure 4: Comparison of determinations of $G_{{\mathrm{L}}}(\tau)$ at finite lattice spacing for a few values of $R_{{\mathrm{s}}}$ with the $R_{{\mathrm{s}}}\to0$-extrapolated continuum correlator $G_{{\mathrm{E}}}(\tau)$. Figure from Ref. Bonanno:2023ljc.
• Figure 5: Example of the calculation of the sphaleron rate for $T=300~\mathrm{MeV} \simeq 1.94 T_c$. Top left panel: Monte Carlo evolution of the cooled clover lattice topological charge for the finest lattice spacing explored at this temperature, $aT=1/14$. Top right panel: continuum limit of $\Gamma_{{\mathrm{L}}}/T^4$ at fixed $\sigma/T=1.75$ and $R_{{\mathrm{s}}} T$ for the three smallest smoothing radii explored. Bottom left panel: smoothing-radius dependence of the continuum results for $\Gamma_{{\mathrm{S}}}/T^4$ (fixed $\sigma/T=1.75$). Bottom right panel: smearing-width dependence of the continuum results for $\Gamma_{{\mathrm{S}}}/T^4$ at fixed $R_{{\mathrm{s}}}/T$ for the three smallest smoothing radii explored. Figures from Ref. Bonanno:2023thi.