The Carrollian limit of ModMax electrodynamics

TL;DR

This paper explores the Carrollian limit of ModMax electrodynamics, revealing its invariance under Carrollian and conformal symmetries, and highlighting the role of the parameter b3 in the magnetic case.

Contribution

It provides the first analysis of the Carrollian limit of ModMax electrodynamics, identifying its symmetry structure and the role of the parameter b3 in the magnetic case.

Findings

The magnetic Carrollian limit is invariant under the Carrollian group and local Carrollian time translations.

The symmetry algebra includes the Conformal Carroll algebra of level 2 in four dimensions.

The theory maintains conformal invariance and duality symmetry in the Carrollian limit.

Abstract

We consider the Carrollian limit of ModMax electrodynamics, namely the limit of vanishing speed of light, for the most general, four-dimensional, duality and conformal invariant electromagnetism. The theory is parameterized by a unique real constant $\gamma$, which remains playing a non-trivial role in the magnetic Carrollian case, while it can be removed in the electric Carrollian contraction, and we therefore focus in the former. Applying the technique of Lie point symmetries, we obtain that the magnetic limit is invariant under the Carrollian group, as well as under the local translation in Carrollian time $x^{0}\rightarrow x^{0\prime}=x^{0}+f\left(x^{i}\right) $ and $x^{i}\rightarrow x^{i\prime}=x^{i}$, with $f$ being an arbitrary function. A diagonal part of the symmetries span the Conformal Carroll algebra of level $2$, $\mathfrak{ccarr}_2$ in four dimensions. Two additional internal symmetries remain in the Carrollian limit of ModMax standing for the conformal invariance of the theory, as well as the invariance under duality transformations.