A supersymmetric nonlinear sigma model analogue of the ModMax theory

A decade ago, it was shown that associated with any model for U(1) duality-invariant nonlinear electrodynamics there is a unique U(1) duality-invariant supersymmetric nonlinear sigma model formulated in terms of chiral and complex linear superfields. Here we study the N = 1 superconformal σ-model analogue of the conformal duality-invariant electrodynamics known as the ModMax theory. We derive its dual formulation in terms of chiral superfields and show that the target space is a Kähler cone with U(1) × U(1) being the connected component of the isometry group.