Coupling the precursor of the most general theory of electromagnetism invariant under duality and conformal invariance with scalars, and BIon-type solutions

Recently, the most general theory of electromagnetism invariant under duality and conformal invariance was written, and dubbed ModMax. It arises from a generalization of Born-Infeld (BI) theory by taking the infinite tension limit, T→∞. In this paper we show that this generalization can be obtained from a branelike construction, just like BI, and can thus be coupled to scalars in the same way to obtain a Dirac-Born-Infeld (DBI)-like action. All the BIon and catenoid solutions, and their interpolations, are still solutions of the generalized DBI-like action, suggesting that an interpretation within string theory could be possible. We also show that Ra\~nada's knotted solutions (with nonzero helicities) are still valid, both in the ModMax theory, and in its precursor.