Multipoint correlators of conformal field theories: implications for quantum critical transport

We relate three-point correlators between the stress-energy tensor and conserved currents of conformal field theories (CFTs) in 2+1 dimensions to observables of quantum critical transport. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then do the computation using holography. In the holographic approach, the correlators are computed from an effective action on 3+1 dimensional anti-de Sitter space (AdS$_4$), and depend upon the co-efficient, $\gamma$, of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus fixing the values of $\gamma$. The CFTs of free fermions and bosons take the values $\gamma=1/12,-1/12$ respectively, and so saturate the bound $|\gamma| \leq 1/12$ obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of $\gamma$. The value of $\gamma$ also controls the frequency dependence of the conductivity, and other properties of quantum-critical transport at non-zero temperatures. Our results for the values of $\gamma$ lead to an appealing physical interpretation of particle-like or vortex-like transport near quantum phase transitions of interest in condensed matter physics.