Non-renormalisation and Universality of Anomalous Conductivities

Abstract

The chiral current in a quantum field theory is anomalous. This anomaly generates currents proportional to the magnetic field and the vorticity. The conductivities, the proportionality constants, can be determined almost completely in hydrodynamic approximation, but there remains an undetermined contribution proportional to the temperature squared. We investigate whether this coefficient renormalises and whether it is universal. It has been calculated for a free theory and a strongly coupled theory in [1]. The strong coupling computation done using the AdS/CFT correspondence, for a black hole with a gauge field and (gravitational-) Chern-Simons terms. They find the same for weak and strong coupling, showing that for this model it does not renormalise. We consider a holographic model which also incorporates a scalar field. This model has a free parameter determining the scalar potential. For one value the scalar field vanishes and we return to the previous case. We have computed the conductivities analytically for two other values. We find exactly the same conductivities. This shows that in these cases also, the conductivities do not renormalise, and suggests that they are universal in the sense that they do not depend on the microscopic details of the theory.