Anomalous Dimensions for Conserved Currents in Strange Metals*

For the past 30 years, the transport properties in the unusual metallic phase seen in the cuprate superconductors and many other quantum critical metals have defied an explanation in terms of the standard building blocks of modern physics --- particles with local interactions and conservation laws. A recent proposal suggests that all of the properties of such `strange metals' can be understood if the current has an anomalous dimension not determined simply by dimensional analysis. My talk will focus on trying to understand this claim. To demystify this claim, I will first show that even in the standard formulation of electricity and magnetism, there is an extra degree of freedom, which has remained unnoticed until now, that can allow, in principle, for the current to have any allowable dimension. This extra degree of freedom is a consequence of Noether's Second Theorem. However, I will show that the only quantum theories to date which exhibit such odd behaviour are holographic models that are derived from a gravity theory that lives in higher dimensions. The existence of currents having anomalous dimensions, a direct probe of the existence of extra `hidden' dimensions, can be tested with the Aharonov-Bohm effect. I will describe this effect and its potential impact for unlocking the secret of the strange metal in the cuprates.