Null Dimensional Reduction of M2-Brane

Abstract

We perform a general reduction of an M2-brane on a space-time that admits a null Killing vector leading to fundamental string and D2-brane action in Newton-Cartan background.

Note About Null Dimensional Reduction of M5-Brane

“…Then we will be able to perform duality transformation as in case of the spatial dimensional reduction and we argue that resulting action corresponds to D4-brane in torsional Newton-Cartan background. This is main result of this paper that together with the paper [17] show that extended objects in M-theory map under null dimensional reductions to fundamental strings an D-branes in torsional Newton-Cartan string theory. It is very interesting that these actions have functionally the same form as their relativistic counterparts since they depend on the pull-back of the Newton-Cartan volume form [20].…”

“…The action (3.34) or its alternative form (3.39) is final form of non-relativistic D4-brane action in the background that arises by null dimensional reduction of M-theory. The kinetic part of the action has standard DBI like form and has functionally the same form as D2brane action in torsional Newton-Cartan background that was found in [17]. There is also an additional WZ like term that has an exceptional property that it depends on the world-volume fields v α , h αβ .…”

“…On the other hand we can ask the question how extended objects in M-theory map under null dimensional reductions. In our previous paper [17] we studied null dimensional reduction of M2-brane. We showed that when we have M2-brane wrapped null direction we get fundamental string action in torsional Newton-Cartan string theory.…”

Canonical Analysis of New Non-Relativistic String Action and Uniform Light-Cone Gauge Formulation

“…This proposal was subsequently studied in many papers, see for example [32,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Another, seemeangly different approach for definition of non-relativistic string theory, was presented in remarkable paper [4] where non-relativistic string in torsional Newton-Cartan background was defined by null dimensional reduction from higher dimensional space-time with light-like isometry, for further works see for example [21,22,23,24,25,26,27,28,29,30,31]. Finally the relation between these two seamingly different non-relativistic string theories was found in [13].…”

Torsional string Newton-Cartan geometry for non-relativistic strings

“…See e.g [53,54]. and[55] for recent work on non-relativistic M-branes using null reduction and limits respectively.…”