Interacting Conformal Carrollian Theories: Cues from Electrodynamics

TL;DR

This paper develops a conformally invariant Carrollian electrodynamics framework, constructing free and interacting Lagrangians that respect infinite-dimensional symmetries without gauge redundancies.

Contribution

It introduces a novel method to build Carrollian electrodynamics with conformal invariance, including new fields and exact symmetry realization at the charge algebra level.

Findings

Constructed free magnetic sector Lagrangian using Helmholtz integrability.

Added conformally invariant quartic interaction terms.

Achieved exact realization of infinite-dimensional symmetry algebra without central extensions.

Abstract

We construct the free Lagrangian of the magnetic sector of Carrollian electrodynamics. The construction relies on Helmholtz integrability condition for differential equations in a self consistent algorithm, working hand in hand with imposing invariance under infinite dimensional Conformal Carroll algebra. It requires inclusion of new fields in the dynamics and the system is free of gauge redundancies. We next add interaction (quartic) terms to the free Lagrangian, strictly constrained by conformal invariance and Carrollian symmetry. The dynamical realization of the non-semi simple infinite dimensional symmetry algebra at the level of charge algebra is exact and free from central terms.