  We study the Langevin dynamics of a U(1) lattice gauge theory on the torus,
and prove that they converge for short time in a suitable gauge to a system of
stochastic PDEs driven by space-time white noises. This also yields convergence
of some gauge invariant observables on a short time interval. We fix gauge via
a DeTurck trick, and prove a version of Ward identity which results in
cancellation of renormalization constants that would otherwise break gauge
symmetry. The proof relies on a discrete version of the theory of regularity
structures.
