Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant

Abstract

In this work, we present the three-dimensional Maxwell Carroll gravity by considering the ultra-relativistic limit of the Maxwell Chern-Simons gravity theory defined in three spacetime dimensions. We show that an extension of the Maxwellian Carroll symmetry is necessary in order for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate. Consequently, we discuss the origin of the aforementioned algebra and theory as a flat limit. We show that the theoretical setup with cosmological constant yielding the extended Maxwellian Carroll Chern-Simons gravity in the vanishing cosmological constant limit is based on an enlarged extended version of the Carroll symmetry. Indeed, the latter exhibits a non-degenerate invariant tensor allowing the proper construction of a Chern-Simons gravity theory which reproduces the extended Maxwellian Carroll gravity in the flat limit.

18 pages

References in corpus (16)

• The BMS/GCA correspondence
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Flat Holography: Aspects of the dual field theory
• Expanding Lie (super)algebras through abelian semigroups
• Field Theories with Conformal Carrollian Symmetry
• Warped Conformal Field Theory as Lower Spin Gravity
• Generalized cosmological term from Maxwell symmetries
• Deformations of Maxwell algebra and their Dynamical Realizations
• Super-BMS${}_3$ algebras from $\mathcal{N}=2$ flat supergravities
• N=1 Supergravity and Maxwell superalgebras
• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Generalized Pure Lovelock Gravity
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• On the Supersymmetric Extension of Gauss-Bonnet like Gravity
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• Chern-Simons gravity, based on a non-semisimple group