Do the Cuprates Harbor Extra Dimensions?

We all learned that conserved quantities such as current have dimensions that are determined solely by dimensional analysis. For the past 30 years, the cuprate superconductors have defied explanation in terms of the standard building blocks of modern physics, particles with local interactions. A recent proposal for the strange metal in the cuprates suggests that all of the properties 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 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.  However, I will show that the only quantum theories to date which exhibit such behaviour are holographic models that are derived from a gravity theory that lives in an extra dimension. The existence of currents having anomalous dimensions, a direct probe of the existence of extra dimensions,  can be tested with the Aharonov-Bohm effect.  I will describe this effect and its potential impact for unlocking the physics of the strange metal in the cuprates.