Strange Metals and Anomalous Dimensions for Conserved Currents

The unsaturating resistivity exceeding the Ioffe-Regel-Mott bound in the strange metal phase of the cuprates implies that electrons are not the propagating degrees of freedom. The search for new degrees of freedom has led some to conclude that not only does the relevant gauge field that describes the interactions with electromagnetic radiation have an anomalous dimension but so does the current. This conclusion flies in the face of the well known result in quantum field theory that conserved quantities do not acquire anomalous dimensions under any amount of renormalization. My talk will focus on demistifying the claim of anomalous dimensions of conserved quantities. I will show that N\"other's Second Theorem[1,2] actually allows for electromagnetisms in which the conserved current and gauge field can actually have arbitrary dimensions. Specific models are constructed which exhibit such anomalies[1,2]. I will show that the resulting Aharonov-Bohm effect deviates strongly from the standard result and hence can be used a sharp test of anomalous dimensions in the strange metal phase of the cuprates.

1.) G. La Nave, K. Limtragool, P. W. Phillips, ``Fractional Electromagnetism in Quantum Matter and High-Energy Physics,'' Rev. Mod. Phys., vol. 91, 021003 (2019).

2.) G. La Nave and P. W. Phillips, ``Anomalous Dimensions for Boundary Conserved Currents in Holography via the Caffarelli-Silvestri Mechanism for p-forms,'' Comm. Math. Physics, 366(1), 119-137 (2019).

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