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We consider the matrix model associated with pp-wave background and constructsupersymmetric branes. In addition to the spherical membrane preserving 16supersymmetries, one may construct rotating elliptic membranes preserving 8supersymmetries. The other branch describes rotating 1/8 BPS hyperbolic branesin general. When the angular momentum vanishes in this branch, the hyperbolicbrane becomes 1/4 BPS preserving 8 real supersymmetries. It may have the shapeof hyperboloid of one or two sheets embedded in the flat three space. We studythe spectrum of the worldvolume fields on the hyperbolic branes and show thatthere are no massless degrees. We also compute the spectrum of the 0-2 strings.Comment: 14 pages, 1 figure, references added, typos correcte

Supersymmetric branes in the matrix model of appwave background