Critical dynamics, duality, and the exact dynamic exponent in extreme type II superconductors

The critical dynamics of superconductors is studied using renormalization group and duality arguments. We show that in extreme type II superconductors the dynamic critical exponent is given exactly by $z=3/2$. This result does not rely on the widely used models of critical dynamics. Instead, it is shown that $z=3/2$ follows from the duality between the extreme type II superconductor and a model with a critically fluctuating gauge field. Our result is in agreement with Monte Carlo simulations.