  We demonstrate quite generally how a conserved current can have an anomalous
dimension. We show here that if the current in the normal state of the cuprates
has an anomalous dimension, then the Aharonov-Bohm flux through a ring does not
have the standard $eBA/\hbar$ form, where $A$ is the area and $B$ the external
magnetic field, but instead is modified by a geometrical factor that depends
directly on the anomalous dimension of the current. We calculate the signal 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.
