Horizon universality and anomalous conductivities

Abstract

We show that the value of chiral conductivities associated with anomalous transport is universal in a general class of strongly coupled quantum field theories that admit a gravitational holographic dual in the large N limit. Our result only applies to theories in the presence of external gauge fields with no dynamical gluon fields. On the gravity side the result follows from near horizon universality of the fluctuation equations, similar to the holographic calculation of the shear viscosity.

Universality of anomalous conductivities in theories with higher-derivative holographic duals

“…More recently, these calculations were generalised to cases of nonconformal holography (in which T µ µ = 0), giving the same results [56,57]. A way to think of such holographic setups is as of geometric realisations of the renormalisation group flows.…”

“…in [54] and many other holographic studies. To express all four anomalous conductivities purely in terms of the near-horizon data, our work will generalise the membrane paradigm result for the chiral magnetic conductivity of Gürsoy and Tarrío [57]. This will then enable us to establish the universality of the four transport coefficients in the presence of a general higher-derivative bulk theory specified in section 2.…”

“…Recently, a work by Gürsoy and Tarrío [57] made the first step in this direction by proving the universality of chiral magnetic conductivity σ JB in a two-derivative EinsteinMaxwell-dilaton theory with an arbitrary scalar field potential and anomaly-inducing Chern-Simons terms. The only necessary assumptions were that the bulk geometry is asymptotically anti-de Sitter (AdS) and that the Ricci scalar at the horizon must be regular.…”

“…What we will show is that the expressions (1.4), (1.5) and (1.6) remain universal in any higher-derivative theory so long as the action (excluding the ChernSimons terms) is gauge-and diffeomorphism-invariant. 6 All we will assume, in analogy with [57], is that the bulk theory is asymptotically AdS (it has a UV conformal fixed point) and that it permits a black brane solution with a regular, non-extremal horizon. In its essence, the proof will reduce to showing the validity of the membrane paradigm and then a study of generic, higher-derivative effective theories (all possible terms present in the conserved current) at the horizon and the boundary (as depicted in figure 1).…”

“…As in [57], the membrane paradigm equations follow from the two Maxwell's equations in (2.9). For conciseness, we only show the details of the axial current computation, which involves H 5 from eq.…”