Abstract
In this short note we study null dimensional reduction of M5-brane covariant action. We analyze longitudinal dimensional reduction that leads to nonrelativistic D4-brane and transverse reduction that leads to NS5-brane in nonrelativistic string theory.
Highlights
AND SUMMARYIt has been known from the late 1990s that string theories have origin in eleven dimensional theory: M-theory [1]
Since all string theories can be considered as limits of M-theory it is clear that M-theory has to contain extended objects that are parent objects of fundamental strings, D-branes and NS5-branes [2], for review see for example [3]
The fundamental object of M-theory is M2-brane as string is fundamental for string theory since M2-brane electrically couples to three form Cð3Þ in the same way as string couples to two form Bð2Þ
Summary
It has been known from the late 1990s that string theories have origin in eleven dimensional theory: M-theory [1]. We will be able to perform duality transformation as in the case of the spatial dimensional reduction and we argue that the resulting action corresponds to a D4-brane in the torsional Newton-Cartan background. This fact raises a very important question which is a relation between D4-brane action derived in this paper and the form of nonrelativistic Dp-brane in torsional Newton-Cartan (NC) background as was found in [20,21] In these papers the nonrelativistic Dp-brane in torsional NC background was found by T-duality from relativistic Dðp þ 1Þ-brane in the background with lightlike isometry when this Dðp þ 1Þ-brane is extended along the lightlike dimension and we perform T-duality along it.. The resulting action should correspond to a NS5-brane in torsional Newton-Cartan string theory as transverse dimensional reduction of the M5-brane along a spatial circle corresponds to a NS5-brane in type IIA theory
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