Compensator-free $\mathcal{N}=2$ extension of ModMax and scalar propagation

We construct a compensator-free $\mathcal{N}=2$ superconformal and electric–magnetic duality-invariant extension of ModMax electrodynamics in ordinary flat superspace. The action is built entirely from the Abelian vector multiplet, using a derivative composite of its field strength, and the self-duality equation is solved to all orders as a formal series in the coupling. Upon setting the additional $\mathcal{N}=1$ chiral multiplet to zero, the action is equivalent off shell to the $\mathcal{N}=1$ ModMax action of Bandos, Lechner, Sorokin and Townsend through a local vector-prepotential redefinition. Since the complex scalar of the $\mathcal{N}=2$ multiplet is set to zero in this reduction, we add one superconformal interaction that leaves the reduction unchanged and is chosen to ensure causal scalar propagation. On constant non-null electromagnetic backgrounds with vanishing scalar expectation value, the higher-order scalar coefficients are fixed by requiring the scalar quadratic action to satisfy the stress-tensor square-root flow, modulo equations of motion and a total derivative. We determine the quadratic action of the full multiplet on these backgrounds to all orders. Its analytic continuation to finite $\gamma \ge 0$ gives causal scalar propagation, with transverse speed squared $e^{-\gamma }$ and unit longitudinal speed, the ModMax photon cones, luminal gauginos with positive kinetic coefficients, and auxiliary fields with algebraic equations of motion.