Multiple M0-brane system in an arbitrary eleven-dimensional supergravity background

Abstract

The equations of motion of multiple M0-brane (multiple M-wave or mM0) systems in an arbitrary D ¼ 11 supergravity superspace, which generalize the matrix model equations for the case of interaction with a generic 11-dimensional supergravity background, are obtained in the frame of the superembedding approach. We also derive the Bogomol'nyi-Prasad-Sommerfeld (BPS) equations for supersymmetric bosonic solutions of these mM0 equations and show that the set of 1=2 BPS solutions contain a fuzzy sphere modeling M2 brane as well as that the Nahm equation appears as a particular case of the 1=4 BPS equations.

Covariant action and equations of motion for the eleven dimensional multiple M0-brane system

“…There exists also the 'backreaction'-the influence of the relative motion on the motion of the center of energy. This is characteristic for the purely bosonic Myers actions [3] and their generalizations [14], but was not catched by the superembedding approach to mM0 system developed in [15,22] because it was based on the standard superembedding approach equation for the center of energy variables. How to change this center of energy superembedding equation to account for 'backreaction' of the relative motion on the center of energy dynamics is one of the interesting problems for future.…”

“…17 The purely bosonic Myers-type action for the mM0 system in a bosonic pp-wave background was proposed in [49]. The supersymmetric and Lorentz covariant equations for mM0 system in pp-wave superspace has been deduced in [23] from the superembedding approach description of [22]. This has been developed for an arbitrary 11D supergravity superspace, but the dynamics of the center of energy in it has been governed by the the same superembedding equation as describing single M0-brane.…”

“…To resume, following [15,22,26] we will describe the center of energy motion of N nearly coincident M0branes (mM0 system) by the 11 commuting and 32 anticommuting coordinate functionŝ…”

“…This implies the necessity to adjust the SO(1, 1) weight also to the fields describing the relative motion of the mM0 constituents. Following [15,22,26] we define the SO(1, 1) weight of the bosonic and fermionic fields to be -2 and -3, respectively, so that in a more explicit notation (and using the conventions were the upper − index indicate the same -1 weight as the lower + one) 9…”

“…therein). The generalization of these equations for the case of mM0-system in curved 11D supergravity superspace, which describes the generalization of the M(atrix) theory [20](see also earlier [21]) for the case of its interaction with arbitrary supergravity background, were presented and studied in [22]. In [23] it was shown that in the case of 11D pp-wave background these equations reproduce (in an approximation) the so-called BMN matrix model proposed for this background by Berenstein, Maldacena and Nastase in [24].…”