On self-dual Carrollian conformal nonlinear electrodynamics

TL;DR

This paper introduces a family of Carrollian ModMax theories of nonlinear electrodynamics that are invariant under duality and conformal transformations, exploring their properties and behavior under specific deformations.

Contribution

It proposes new Carrollian ModMax theories with duality and conformal invariance, deriving their Lagrangians and analyzing their flow under the Tar{T} deformation.

Findings

Theories are invariant under Carrollian (2) duality and conformal transformations.

Deformation flow connects different theories, reaching Maxwell theory as an endpoint.

Constructs scalar theories with similar properties that flow to BMS-invariant models.

Abstract

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 $\text{SO}(2)$ electromagnetic (EM) duality transformations and conformal transformation. We define the Carrollian $\text{SO}(2)$ 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 $\sqrt{T\bar{T}}$ 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 $\sqrt{T\bar{T}}$ flow and may flow to a BMS free multi-scalar model.