Anomalous Dimensions for Gauge Fields in the Strange Metal of the Cuprates

One of the cornerstones of theoretical physics is that conserved currents cannot have anomalous dimensions. However, a recent proposal[1] for the ubiquitous strange metal phase in the cuprates argues just the opposite. Namely, all of the properties of such `strange metals' can be understood if the current has an anomalous dimension. My talk will focus on trying to understand this claim. To demystify this claim, I will first show[2] that even in the standard formulation of gauge theories, there is a loop-hole in Noether's theorems which has remained `almost' (Noether was aware of it) un-noticed until now, that can allow, in principle, for the current to have any allowable dimension. 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 corresponding boundary theory is inherently non-local as dictated by the exception to Noether's theorems. 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.