New applications of the chiral anomaly 1

We describe consequences of the chiral anomaly in the theory of quantum wires, the (quantum) Hall effect, and of a four-dimensional cousin of the Hall effect. We explain which aspects of conductance quantization are related to the chiral anomaly. The fourdimensional analogue of the Hall effect involves the axion field, whose time derivative can be interpreted as a (space-time dependent) difference of chemical potentials of lefthanded and right-handed charged fermions. Our four-dimensional analogue of the Hall effect may play a significant rôle in explaining the origin of large magnetic fields in the (early) universe. 1 What is the chiral anomaly? The chiral abelian anomaly has been discovered, in the past century, by Adler, Bell and Jackiw, after earlier work on π-decay starting with Steinberger and Schwinger; see e.g. [1] and references given there. It has been rederived in many different ways of varying degree of mathematical This review is dedicated to the memory of Louis Michel, the theoretician and the friend.