Anomalous dimension of the electrical current in strange metals from the fractional Aharonov-Bohm effect

We show here that if the current in the strange metal phase of the cuprates has an anomalous dimension, then the Aharonov-Bohm flux through a ring does not have the standard form, where A is the area, B is the external magnetic field, and e is the electric charge, but instead it is modified by a geometrical factor that depends directly on the anomalous dimension of the current. We calculate the Aharonov-Bohm flux in square and disk geometries. In both cases, the deviation from the standard result is striking and offers a fingerprint about what precisely is strange about the strange metal.