Maxim Chernodub - Transport effects due to scale anomaly

We overview transport phenomena generated by the scale anomaly in interacting quantum field theories of massless (chiral) particles with emphasis on Dirac and Weyl semimetals in the limit of zero temperature and chemical potential. First, we discuss anomaly-induced thermoelectric effects in the background of the magnetic field in the presence of a temperature gradient. Second, we consider systems with boundaries, where the scale anomaly produces electric edge current, which is related to the Schwinger effect and gives rise to unusual, polynomial-type charge screening. The magnitude of all these phenomena is proportional to the beta function associated with the renormalization of electric charge. In contrast to the axial and axial-gravitational anomalies, the scale-anomalous response is not quantized.