Abstract
We construct the canonical action of a Carroll string doing the Carroll limit of a canonical relativistic string. We also study the Killing symmetries of the Carroll string, which close under an infinite dimensional algebra. The tensionless limit and the Carroll $p$-brane action are also discussed.
Highlights
In either of the two limits, the Carroll string exhibits a trivial dynamics like the Carroll particle
If we consider Carroll strings coupled to Carroll gravity the strings will have a nontrivial dynamics like in the case of the Carroll particle coupled to Carroll gauge fields [27]
Notice as a feature of the rescaling ω → ∞ of the relativistic string to obtain the Carroll string that if we dimensionally reduce the Carroll string to the Carroll particle, this reduction at the level of the Killing symmetries does not reproduce the infinite-dimensional symmetry for transverse fields which exists in the particle case [27]
Summary
In order to obtain the Carroll action for the string we take the ‘stringy’ Carrollian limit by rescaling the longitudinal coordinates xμ (μ = 0, 1) with a dimensionless parameter ω: xμ. Where (ωμν, ωμi, ωij, ζμ, ζi) are respectively the Lorentz boosts in the two longitudinal directions, the time and space Carroll boosts, the spatial rotations, longitudinal translations and the transverse translations. These transformations can all be derived from a general infinitesimal Poincare transformation, δxM = ωMN xN +ξM and δpM = ωMN pN , by performing the rescaling xμ λ ωμi. If we consider Carroll strings coupled to Carroll gravity the strings will have a nontrivial dynamics like in the case of the Carroll particle coupled to Carroll gauge fields [27]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
