Abstract
We explore Carroll limit corresponding to M2 as well as M3 branes propagating over 11D supergravity backgrounds in M theory. In the first part of the analysis, we introduce the membrane Carroll limit associated to M2 branes propagating over M theory supergravity backgrounds. Considering two specific M2 brane embeddings, we further outline the solutions corresponding to the Hamilton’s dynamical equations in the Carroll limit. We further consider the so called stringy Carroll limit associated to M2 branes and outline the corresponding solutions to the underlying Hamilton’s equations of motion by considering specific M2 brane embeddings over 11D target space geometry. As a further illustration of our analysis, considering the Nambu-Goto action, we show the equivalence between different world-volume descriptions in the Carroll limit of M2 branes. Finally, considering the stringy Carroll limit, we explore the constraint structure as well as the Hamiltonian dynamics associated to unstable M3 branes in 11D supergravity and obtain the corresponding effective world-volume description around their respective tachyon vacua.
Highlights
Hamiltonian formulationWe introduce the pullback of the background fields on the world-volume of the membrane, Gmn = gMN (X)∂mXM ∂nXN ; C012 = CMNP(X)∂0XM ∂1XN ∂2XP (2.3)
Other hand, it is 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]
In the first part of the analysis, we introduce the membrane Carroll limit associated to M2 branes propagating over M theory supergravity backgrounds
Summary
We introduce the pullback of the background fields on the world-volume of the membrane, Gmn = gMN (X)∂mXM ∂nXN ; C012 = CMNP(X)∂0XM ∂1XN ∂2XP (2.3). Λms are the Lagrange multipliers and T2 is the tension associated with the M2 branes. Where we introduce the following constraint (corresponding to the Lagrange multiplier ζ),. We have the following primary Hamiltonian constraint for the system, HP λ0T22 N det Gij. where, Hcan is the standard canonical Hamiltonian and λis the so called Lagrange multiplier in the presence of primary constraint(s) (Γ) such that, HP ≈ Hcan. The other constraint proportional to Π.∂X is not quite apparent in this setup. Notice that this a particular feature of the starting action (2.2). Using a trivial field redefinition, we show that these two formulations are essentially equivalent to each other
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