Emergence of L7-branes and fuzzy S in compactification scenarios of M(atrix) theory

The M(atrix) theory contains membranes and longitudinal 5-branes (L5-branes) as extended objects. The transverse components of these brane solutions can be described by fuzzy CP (k = 1, 2), where k = 1 corresponds to spherical membranes and k = 2 to L5-branes of CP×S1 world-volume geometry. In addition to these, we show the existence of L7-branes of CP×S1 geometry, introducing extra potentials to the M(atrix) theory Lagrangian. As in the cases of k = 1, 2, these L7-branes (corresponding to k = 3) also break the supersymmetries of M(atrix) theory. The extra potentials are introduced such that the energy of a static L7-brane solution becomes finite in the large N limit. As a consequence, fluctuations from the static L7-branes are suppressed, which effectively describes compactification of M(atrix) theory down to 7 dimensions. We show that one of the extra potentials can be considered as a matrix-valued 7-form. The presence of the 7-form in turn supports a possibility of Freund-Rubin type compactification in M(atrix) theory. Compactification down to fuzzy S is also discussed and a realistic matrix model of M-theory in four dimensions is obtained. Current address: Cereja Technology Co., Ltd. 3-1 Tsutaya-Bldg. 5F, Shimomiyabi-cho Shinjuku-ku, Tokyo, 162-0822, Japan ([email protected])