Understanding anomalous particle production in massless QED via time-varying $\theta$ angle

TL;DR

This paper investigates how time-varying $ heta$ angles in massless QED lead to chiral charge generation, especially around magnetic monopoles and fluxes, with implications for baryogenesis, by reducing the problem to 2D QED.

Contribution

It demonstrates the occurrence of chiral charge generation in massless QED with time-dependent $ heta$, clarifying the role of axion-like degrees of freedom and backreaction effects.

Findings

Chiral charge is generated around monopoles, canceling the Witten effect.

Uniform magnetic flux leads to non-trivial time-dependent backreaction.

Results have implications for baryogenesis mechanisms.

Abstract

The Maxwell equations imply that, under the background of non-zero $\boldsymbol{B}$, varying $\theta$ term produces $\boldsymbol{E} \cdot \boldsymbol{B}$. An interesting example is the Witten effect where a magnetic monopole becomes a dyon which, however, should disappear in the exact massless limit of the fermion. Underlying mechanism of this phenomenon has been understood by Callan by the presence of an effective axion-like degree of freedom around the monopole, which is roughly the phase of the fermions. The configuration of this axion cancels the effect of the $\theta$ term. Now, the chiral anomaly implies that non-vanishing $\boldsymbol{E} \cdot \boldsymbol{B}$ induces the chiral charge in the system. The question is whether the chiral charge is generated in the massless limit when we take into account the axion-like degree of freedom in the discussion. The discussion is relevant for the mechanism of baryogenesis under the background of time-dependent $\theta$. We solve the system of the massless QED with time dependent $\theta$ by reducing it to the two-dimensional QED. We demonstrate the occurrence of chiral charge generation in the background of static magnetic field for two cases: a magnetic monopole and a uniform magnetic flux. For the monopole case, the chiral charge comes out from the monopole while canceling the Witten effect. For the case of the uniform flux, on the other hand, the effect of the backreaction cannot be ignored, giving a more non-trivial time dependence. We also discuss their implications on baryogenesis.