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We present new possibilities for the charge response in the quantum criticalregime in 2+1D using holography, and compare them with field theory and recentquantum Monte Carlo results. We show that a family of (infinitely many) higherderivative terms in the gravitational bulk leads to behavior far richer thanwhat was previously obtained. For example, we prove that the conductivitybecomes unbounded, undermining previously obtained constraints. We further finda non-trivial and infinite set of theories that have a self-dual conductivity.Particle-vortex or S duality plays a key role; notably, it maps theories with afinite number of bulk terms to ones with an infinite number. Many propertiessuch as sum rules and stability conditions are proved.

Quantum critical charge response from higher derivatives: is more different?