Higher-dimensional geometries from matrix brane constructions

Matrix descriptions of even-dimensional fuzzy spherical branes S-2k in Matrix Theory and other contexts in type II superstring theory reveal, in the large N limit, higher-dimensional geometries SO(2k + 1)/U(k), which have an interesting spectrum of SO(2k + 1) harmonics and can be up to 20-dimensional, while the spheres are restricted to be of dimension less than 10. In the case k = 2, the matrix description has two dual field theory formulations. One involves a field theory living on the non-commutative coset SO(5)/U(2) which is a fuzzy S-2 fibre bundle over a fuzzy S-4. In the other, there is a U(n) gauge theory on a fuzzy S-4 with O(n(3)) instantons. The two descriptions can be related by exploiting the usual relation between the fuzzy two-sphere and U(n) Lie algebra. We discuss the analogous phenomena in the higher-dimensional cases, developing a relation between fuzzy SO(2k)/U(k) cosets and unitary Lie algebras. (C) 2002 Published by Elsevier Science B.V.