Remark about non-relativistic p-brane

Abstract

We define a different non-relativistic limit of pbrane with the help of canonical form of the p-brane action. We discuss the properties of these actions and their symmetries.

Remark about non-relativistic string in Newton-Cartan background and null reduction

“…Non-relativistic strings were firstly introduced from different point of view in [11,12], for further analysis in the context of string theory, see for example [13,14,15,16,17]. Non-relativistic strings and p-branes gained renewed interest recently when these objects were studied in the context of Newton-Cartan gravity and Carroll gravity [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33].…”

A new action for nonrelativistic particle in curved background

“…A fundamental example is the formulation of an action for a NR particle that couples with gravity [7,11,17]. It forms the basis of coupling more and more sophisticated theories ( like superparticles or even (super)strings) with background gravity [18].…”

“…It forms the basis of coupling more and more sophisticated theories ( like superparticles or even (super)strings) with background gravity [18]. The action formalism for the NR particle has been discussed in the literature [7,11,17], following the methods outlined above. However the result, as shown here, fails on both counts on not having the appropriate transformation for the Newton Cartan metric and having inconsistencies in its passage to the flat limit.…”

“…The lagrangian (6) can be put in a more suggestive form that is frequently used in the literature [11,17,18],…”

Note about Hamiltonian formalism for Newton–Cartan string and p-brane

“…For some recent works, see[9,10,11,12,13,14,15,16,17] 2. For recent work, see for example[32,33,34,35].…”