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We compute three-point correlators between the stress-energy tensor andconserved currents of conformal field theories (CFTs) in 2+1 dimensions. Wefirst compute the correlators in the large-flavor-number expansion of conformalgauge theories and then do the computation using holography. In the holographicapproach, the correlators are computed from an effective action on 3+1dimensional anti-de Sitter space (AdS_4) proposed by Myers et al., and dependupon the co-efficient, \gamma, of a four-derivative term in the action. We finda precise match between the CFT and the holographic results, thus fixing thevalues of \gamma. The CFTs of free fermions and bosons take the values\gamma=1/12,-1/12 respectively, and so saturate the bound |\gamma| <= 1/12obtained earlier from the holographic theory; the correlator of the conservedgauge flux of U(1) gauge theories takes intermediate values of \gamma. Thevalue of \gamma also controls the frequency dependence of the conductivity, andother properties of quantum-critical transport at non-zero temperatures. Ourresults for the values of \gamma lead to an appealing physical interpretationof particle-like or vortex-like transport near quantum phase transitions ofinterest in condensed matter physics.This paper includes appendices reviewingkey features of the AdS/CFT correspondence for condensed matter physicists.

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