Conformal invariance in driven diffusive systems at high currents

We consider space-time correlations in driven diffusive systems which undergo a fluctuation into a regime with an atypically large current or dynamical activity. For a single conserved mass we show that the spatio-temporal density correlations in one space dimension are given by conformally invariant field theories with central charge $c=1$, corresponding to a ballistic universality class with dynamical exponent $z=1$. We derive a phase diagram for atypical behaviour that besides the conformally invariant regime exhibits a regime of phase separation for atypically low current or activity. On the phase transition line, corresponding to typical behaviour, the dynamics belongs to the Kardar-Parisi-Zhang universality class with dynamical exponent $z=3/2$, except for a diffusive point with $z=2$. We demonstrate the validity of the theory for the one-dimensional asymmetric simple exclusion process with both periodic and open boundaries by exact results for the dynamical structure in the limit of maximal current.