Anomaly and long-range forces

Abstract

We consider infrared dependences of chiral effects, like chiral magnetic effect, in chiral media. The main observation is that there exist competing infrared-sensitive parameters, sometimes not apparent. The value of the chiral effects depends in fact on the actual hierarchy of the parameters. Some examples have been already given in the literature. We argue that magnetostatics of chiral media with a non-vanishing chiral chemical potential $\mu_5\neq 0$ is also infrared sensitive. In particular, the system turns to be unstable if the volume is large enough. The instability is with respect to the decay of the system into domains of non-vanishing magnetic field with non-trivial helicity.