Carroll versus Galilei from a brane perspective

Abstract

We show that our previous work on Galilei and Carroll gravity, apt for particles, can be generalized to Galilei and Carroll gravity theories adapted to p-branes (p = 0, 1, 2, ⋯). Within this wider brane perspective, we make use of a formal map, given in the literature, between the corresponding p-brane Carroll and Galilei algebras where the index describing the directions longitudinal (transverse) to the Galilei brane is interchanged with the index covering the directions transverse (longitudinal) to the Carroll brane with the understanding that the time coordinate is always among the longitudinal directions. This leads among other things in 3D to a map between Galilei particles and Carroll strings and in 4D to a similar map between Galilei strings and Carroll strings. We show that this formal map extends to the corresponding Lie algebra expansion of the Poincaré algebra and, therefore, to several extensions of the Carroll and Galilei algebras including central extensions. We use this formal map to construct several new examples of Carroll gravity actions. Furthermore, we discuss the symmetry between Carroll and Galilei at the level of the p-brane sigma model action and apply this formal symmetry to give several examples of 3D and 4D particles and strings in a curved Carroll background.

Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity

“…This relation generalises the known duality between Galilean and Carrollian symmetries[48] in the flat case, see also[42,49].…”

Null reductions of the M5-brane

“…In contrast, the field theories we obtain do not have higher derivatives but involve Lagrange multiplier constraints that reduce the dynamics to motion on a moduli space of anti-selfdual gauge fields [9,10], in line with the DLCQ description of the M5-brane [11,12]. Other classes of theories without Lorentz invariance but related to String/M-Theory have recently received attention in works such as [13][14][15][16][17][18].…”

“…where T IJ is an invariant tensor of Q. This modification leads to 16) whereR M N IJ is the curvature ofΩ IJ M . Thus, to obtain a supersymmetric reduction we must ensureD M =Γ M η, ∂ + = 0 and arrange for suitable choices of curvature and T IJ so that the terms in δS matter cancel.…”

Non-relativistic limit of gravity theories in the first order formalism

“…In contrast, it is also possible to take the ultra-relativistic (UR) limit of gravity and describe the motion of particles with extremely high energies traveling very close to the speed of light, at a strong field regime. Such regime is known as Carroll gravity, see [15][16][17][18][19].…”

“…On the other hand, Carroll gravity arises by taking the relative velocities between frames to approach to the light speed while the light speed tends to zero [15][16][17][18][19]. Therefore, the Carroll limit assumes the full closing of the light cones.…”