A holographic model for quantum critical responses

We analyze the dynamical response functions of strongly interacting quantum critical states described by conformal field theories (cfts). we construct a self-consistent holographic model that incorporates the relevant scalar operator driving the quantum critical phase transition. focusing on the finite temperature dynamical conductivity σ(ω, t ), we study its dependence on our model parameters, notably the scaling dimension of the relevant operator. it is found that the conductivity is well-approximated by a simple ansatz proposed in [1] for a wide range of parameters. we further dissect the conductivity at large frequencies ω ≫ t using the operator product expansion, and show how it reveals the spectrum of our model cft. our results provide a physically-constrained framework to study the analytic continuation of quantum monte carlo data, as we illustrate using the o(2) wilson-fisher cft. finally, we comment on the variation of the conductivity as we tune away from the quantum critical point, setting the stage for a comprehensive analysis of the phase diagram near the transition.