Dynamics of Carroll strings

Abstract

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.

Carroll membranes

“…This therefore should clearly provide enough motivation for exploring the corresponding scenario in case of extended objects like p branes. In other words, unlike in the previous examples [11], one should expect a different dynamics to pop up in the Carroll limit of extended objects like strings and p branes. The purpose of the present article is therefore to address these issues considering specific examples of M2 as well as tachyonic M3 branes in M theory.…”

“…Studying Carroll limit for membranes should be regarded as an interesting direction in itself (in contrast to those of strings or p branes [11] studied previously) as it is naturally coupled to the background 3-form gauge fields (C M N P (X)) [25]. More specifically, going back to the previous analysis of [11], we see that there the discussions on Dp branes as well as strings are made without the inclusion of background fields. However, on the other hand, it is also well known that the coupling between Carroll particles to that with background gauge fields unveils non trivial dynamics even when considering the single particle dynamics [8].…”

“…The present article therefore intends to explore all these issues taking specific examples of M2 as well as M3 branes in M theory. We start our analysis in Section 2 by considering M2 brane world-volume theory and thereby taking its subsequent Carroll limit(s) [11]. We outline the solutions corresponding to Hamilton's dynamical equations considering two different embeddings for Carroll M2 branes propagating over 11D target space geometry.…”

Kinematical versus dynamical contractions of the de Sitter Lie algebras

“…The Carroll group has been associated to tachyon dynamics [17][18][19], to Carrollian electromagnetism [20] versus Galilean electromagnetism [21] or to the dynamics of Carroll particles [22] and Carroll strings [23]. The anisotropic Carroll group in two space dimensions (i.e.…”

“…The terminology is related to the fact that Bacry and Lévy-Leblond have, first of all, scaled the velocity-space generators, the velocity-time translation generators and the space-time translation generators by a parameter ò to obtain, in the limit 0   , the respective contractions that we prefer to call velocity-space contractions, velocity-time contractions and space-time contractions. The Lévy-Leblond contraction approach has been also extended to supersymmetry [12] and kinematical superalgebras [13][14][15].Within the corresponding eleven Lie groups, four of them, namely the Galilei group G governing the Newtonian physics (Galilean relativity), the Poincaré group P governing the Einstein physics (special relativity), the Newton-Hooke groups NH ± describing Galilean relativity in the presence of a cosmological constant and the de Sitter Lie groups dS ± governing the de Sitter relativity of a space-time in expansion or oscillating universe, are well known in physics literature.Within the remaining five ones, the Para-Poincaré groups P ± and the Static S are still unknown in physics, but the Para-Galilei group G ± and the Carroll group C are gaining more interest in recent times.The Para-Galilei group has been identified as governing a light spring [16].The Carroll group has been associated to tachyon dynamics [17][18][19], to Carrollian electromagnetism [20] versus Galilean electromagnetism [21] or to the dynamics of Carroll particles [22] and Carroll strings [23]. The anisotropic Carroll group in two space dimensions (i.e.…”