Matrix Membranes and Integrability

Details Matrix Membranes and Integrability Matrix Membranes and Integrability

1997-09-04

arxiv.org/abs/hep-th/9709042v1

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, Latex, uses lamuphys.sty; talk by 1st author at the UIC "Supersymmetry and Integrable Systems" Workshop, Chicago, Ju

Scientific paper

10.1007/BFb0105319

This is a pedagogical digest of results reported in Phys Lett B405 (1997) 37, and an explicit implementation of Euler's construction for the solution of the Poisson Bracket dual Nahm equation. But it does not cover 9 and 10-dimensional systems, and subsequent progress on them [hep-th/9707190]. Cubic interactions are considered in 3 and 7 space dimensions, respectively, for bosonic membranes in Poisson Bracket form. Their symmetries and vacuum configurations are explored. Their associated first order equations are transformed to Nahm's equations, and are hence seen to be integrable, for the 3-dimensional case, by virtue of the explicit Lax pair provided. Most constructions introduced also apply to matrix commutator or Moyal Bracket analogs.

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