Waves and strings in an interacting conformal chiral 2-form theory in six dimensions

In six dimensions there exists a unique one-parameter family of non-linear conformal electrodynamics for a chiral 2-form gauge field which includes (in a free-field limit) the linear chiral 2-form theory and is related, by dimensional reduction, to the four-dimensional ModMax electrodynamics. In this work, we present the first exact solutions of this theory in presence of gravity. In particular, we will consider plane-wave, Robinson-Trautman, and self-dual dyonic string configurations, generalizing well-known solutions of this type in six-dimensional supergravities with linear chiral 2-form multiplets.