Thermoskyrmions

TL;DR

This work shows that finite-temperature effects enable the existence of stable thermoskyrmions—topological solitons stabilized by higher-derivative operators generated in a 3D EFT obtained via dimensional reduction from a non-linear SU(2) sigma model with fermions. By constructing the high-temperature 3D EFT for two electroweak-like toy models and performing 1-loop matching up to $ ext{O}(p^6)$, the authors identify the operators responsible for stabilization and use a neural-network minimization of the hedgehog ansatz to obtain stable configurations with unit winding. They analyze the thermodynamics of these configurations, assess the validity of the 3D EFT expansion, and discuss the semiclassical nature and potential cosmological implications, including dark matter candidates within the SM framework at finite temperature. The results suggest that thermoskyrmions provide a controlled, temperature-driven window into non-perturbative topological objects in the electroweak sector, motivating further study of zero-temperature limits and possible real-world realizations.

Abstract

Skyrmions are stable and topologically non-trivial field configurations that behave like localized particles. They appear in the chiral effective theory for pions, where they correspond to the baryon states, and might also exist in the electroweak theory, in the presence of certain effective interactions. In this paper, focusing on toy models that capture different limits of the electroweak sector of the Standard Model (SM), we show that skyrmions not classically stable at zero temperature can be stabilized by thermal effects. This result motivates the study of skyrmions in the quantum effective action of the SM, potentially implying the existence of dark matter without new physics.

Figures (6)

• Figure 1: Four-derivative physical coefficients $c_1$ and $c_2$ in model A as a function of the Yukawa for fixed $T/v = 1$. The different curves show the 1-loop matching result at different orders in the Yukawa.
• Figure 2: Thermoskyrmion profile that minimizes the rescaled 3D action $\widetilde{S}'_3[\eta]$ subject to boundary conditions $\eta(0)=\pi$ and $\eta(\tilde{r}'_\mathrm{max}=5)=0$; see text for details.
• Figure 3: Ratio between the inverse thermoskyrmion radius $R_\mathrm{TS}^{-1}$ and the thermal scale $\pi T$ (in units of $v$) for $g=1, 0.5, 0.1$ in a range of temperatures. The dashed line marks a very conservative estimate of the breaking of the 3D EFT expansion on the low-temperature side, neglecting the suppression of operators due to their loop-generated WCs.
• Figure 4: Free energy (top left), average energy (top right) and radius (bottom) of a thermoskyrmion in units of $v$ for fixed $g=1$, in the allowed temperature range.
• Figure 5: Ratio $\lambda_\mathrm{th}/R_\mathrm{TS}$ for $g=1,0.5,0.1$, in the allowed temperature range. The dashed line marks the breaking of the assumption of classicality for the thermoskyrmion.