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We derive a dynamic field theory for a kinetically constrained model, based on the Fredrickson-Andersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d⩾2, the behavior of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behavior is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.
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