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

Abstract

We compute three-point correlators between the stress-energy tensor and conserved currents of conformal field theories (CFTs) in 2+1 dimensions. 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) proposed by Myers et al., 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| <= 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.This paper includes appendices reviewing key features of the AdS/CFT correspondence for condensed matter physicists.