On self-dual Carrollian conformal nonlinear electrodynamics

In this work, we study the duality symmetry group of Carrollian (nonlinear) electrodynamics and propose a family of Carrollian ModMax theories, which are invariant under Carrollian SO(2) electromagnetic (EM) duality transformations and conformal transformation. We define the Carrollian SO(2) EM transformations, with the help of Hodge duality in Carrollian geometry, then we rederive the Gaillard-Zumino consistency condition for EM duality of Carrollian nonlinear electrodynamics. Together with the traceless condition for the energy-momentum tensor, we are able to determine the Lagrangian of the Carrollian ModMax theories among pure electrodynamics. We furthermore study their behaviors under the $\sqrt{T\overline{T}}$ \( \sqrt{T\overline{T}} \) deformation flow, and show that these theories deform to each other and may reach two endpoints under the flow, with one of the endpoint being the Carrollian Maxwell theory. As a byproduct, we construct a family of two-dimensional Carrollian ModMax-like multiple scalar theories, which are closed under the $\sqrt{T\overline{T}}$ \( \sqrt{T\overline{T}} \) flow and may flow to a BMS free multi-scalar model.