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We consider a relativistic plasma of fermions coupled to an Abelian gaugefield and carrying a chiral charge asymmetry, which might arise in the earlyUniverse through baryogenesis. It is known that on large length scales,$\lambda \gtrsim 1/(\alpha \mu_5)$, the chiral anomaly opens an instabilitytoward the erasure of chiral charge and growth of magnetic helicity. Here thechemical potential $\mu_{5}$ parametrizes the chiral asymmetry and $\alpha$ isthe fine-structure constant. We study the process of chiral charge erasurethrough the thermal fluctuations of magnetic helicity and contrast with thewell-studied phenomenon of Chern-Simons number diffusion. Through thefluctuation-dissipation theorem we estimate the amplitude and time scale ofhelicity fluctuations on the length scale $\lambda$, finding $\delta\mathcal{H} \sim \lambda T$ and $\tau \sim \alpha \lambda^3 T^2$ for arelativistic plasma at temperature $T$. We argue that the presence of a chiralasymmetry allows the helicity to grow diffusively for a time $t \simT^3/(\alpha^5 \mu_5^4)$ until it reaches an equilibrium value $\mathcal{H} \sim\mu_{5} T^2 / \alpha$, and the chiral asymmetry is partially erased. If thechiral asymmetry is small, $\mu_5 < T/\alpha$, this avenue for chiral chargeerasure is found to be slower than the chiral magnetic effect for which $t \simT / (\alpha^3 \mu_{5}^2)$. This mechanism for chiral charge erasure can beimportant for the hypercharge sector of the Standard Model as well asextensions including ${\rm U}(1)$ gauge interactions, such as asymmetric darkmatter models.

Chiral Charge Erasure via Thermal Fluctuations of Magnetic Helicity