Emergence of longitudinal 7-branes and fuzzy S{sup 4} in compactification scenarios of M(atrix) theory
- Physics Department City College of the CUNY, New York, New York 10031 (United States)
In M(atrix) theory, there exist membranes and longitudinal 5-branes (L5-branes) as extended objects. Transverse components of these brane solutions are known to be described by fuzzy CP{sup k} (k=1, 2), where k=1 and k=2 correspond to spherical membranes and L5-branes of CP{sup 2}xS{sup 1} world-volume geometry, respectively. In addition to these solutions, we here show the existence of L7-branes of CP{sup 3}xS{sup 1} geometry, introducing extra potentials to the M(atrix) theory Lagrangian. As in the cases of k=1, 2, the 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 where N represents the matrix dimension of fuzzy CP{sup 3}. As a consequence, fluctuations from the 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. This suggests that our modification of M(atrix) theory can also lead to a physically interesting matrix model in four dimensions. In hope of such a possibility, we further consider compactification of M(atrix) theory down to fuzzy S{sup 4} which can be defined in terms of fuzzy CP{sup 3}. Along the way, we also find a new L5-brane solution to M(atrix) theory which has purely spherical geometry in the transverse directions.
- OSTI ID:
- 21409354
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 81, Issue 4; Other Information: DOI: 10.1103/PhysRevD.81.046006; (c) 2010 The American Physical Society; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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