Katz, EmanuelSachdev, SubirSørensen, Erik S.Witczak-Krempa, William2015-06-122014Katz, Emanuel, Subir Sachdev, Erik S. Sørensen, and William Witczak-Krempa. 2014. “Conformal Field Theories at Nonzero Temperature: Operator Product Expansions, Monte Carlo, and Holography.” Phys. Rev. B 90 (24) (December). doi:10.1103/physrevb.90.245109.1098-0121http://nrs.harvard.edu/urn-3:HUL.InstRepos:16310007We compute the nonzero temperature conductivity of conserved flavor currents in conformal field theories (CFTs) in 2+1 space-time dimensions. At frequencies much greater than the temperature, ℏω≫kBT, the ω dependence can be computed from the operator product expansion (OPE) between the currents and operators, which acquire a nonzero expectation value at T>0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these large ω results to the corresponding correlators of holographic representations of the CFT: the holographic approach then allows us to extrapolate to small ℏω/(kBT). Other holographic studies implicitly only used the OPE between the currents and the energy-momentum tensor, and this yields the correct leading large ω behavior for a large class of CFTs. However, for the Wilson-Fisher CFT, a relevant “thermal” operator must also be considered, and then consistency with the Monte Carlo results is obtained without a previously needed ad hoc rescaling of the T value. We also establish sum rules obeyed by the conductivity of a wide class of CFTs.en-USJournal Article2015-06-1210.1103/PhysRevB.90.245109