Conformal field theories at nonzero temperature: Operator product expansions, Monte Carlo, and holography

Strongly correlated quantum critical points with conformal symmetry in two spatial dimensions describe many phase transitions in condensed matter systems, as for example that from superfluid to insulator. Combining field theory methods, Monte Carlo simulations, and the holographic duality from string theory, the authors use an operator product expansion to derive non-perturbative results for these systems, including the leading terms in the frequency dependence of the nonzero temperature conductivity and sum rules obeyed by the conductivity. These methods and results are applicable to a wide class of conformal field theories for condensed matter systems.