Universal aspects of holographic quantum critical transport with self-duality

We prove several universal properties of charge transport in generic conformal field theories holographic to nonminimal extensions of four-dimensional Einstein-Maxwell theory with exact electromagnetic duality invariance. First, we explicitly verify that the conductivity of these theories at zero momentum is a universal frequency-independent constant. Then, we derive the analytical expressions for the conductivities at nonzero momentum in any holographic duality-invariant theory for large frequencies and in the limit of small frequencies and momenta. Next, in the absence of terms that couple covariant derivatives of the curvature to gauge field strengths, two universal features are proven. On the one hand, it is shown that for a general-relativity neutral black-hole background the conductivities at any frequency and momentum are independent of the choice of duality-invariant theory, thus coinciding with those in the Einstein-Maxwell case. On the other hand, if higher-curvature terms affect the gravitational background, the conductivities get modified, but the contributions from nonminimal couplings of the gauge field to gravity are subleading. We illustrate this feature with an example.

Automated summary

In this article, we prove the universal properties of charge transport in holographic nonminimal extensions of four-dimensional Einstein-Maxwell theory with exact electromagnetic duality invariance. We show that the conductivity is a universal frequency-independent constant at zero momentum and derive analytical expressions for non-zero momentum conductivities in any holographic duality-invariant theory in the limit of large frequencies and small frequencies and momenta. We also demonstrate that the conductivities in a general relativity neutral black-hole background are independent of the choice of duality-invariant theory and the contributions from nonminimal couplings of the gauge field to gravity are subleading.