Plenary Talk 1

Abstract

Symmetries that exist in classical field theory are broken when one enters the quantum regime, i.e. the quantum field theory. This symmetry breaking is referred to as quantum anomalies, of which there are three important ones: axial or chiral anomaly, scale or conformal anomaly, and parity anomaly. Chiral anomaly entails non-conservation of chiral current whereas in the case of scale anomaly it depends on the energy at which it is measured. Similarly, parity anomaly arises when the quantum theory is not invariant under a change of parity. In practice, it is very difficult to test these anomalies in field theory but quantum materials such as Dirac and Weyl semimetals, topological insulators and topological superconductors provide a relatively facile testbed in which to observe signatures of the anomalies in transport measurements under high magnetic fields, strain, light (i.e., ultrafast optics) and by other means, for instance thermal gradients and magneto-thermal measurements. The linear energy-momentum dispersion of Dirac materials in their electronic structure is uniquely suited to extract the anomalous signatures in experiments. This talk will provide a semi-didactic review of the relevant concepts, current progress in this topic, materials, models and measurements.