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

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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.