Regular Seminar Sanjaye Ramgoolam (QMUL)
Recent work on membranes of M-theory has lead to a new type of physical realization of fuzzy 2-spheres in Matrix Brane actions. In standard realizations, the fuzzy two-sphere coordinates transforming in the vector of the spherical rotation symmetry are identified with matrix variables in the adjoint representation of the unitary symmetry of the Matrix brane actions.In these new realizations, spinors of the rotational symmetry are identified with variables in bi-fundamental representations of the unitary symmetry. The vector coordinates of the fuzzy 2-sphere are recovered from bilinears in the spinors by a fuzzy version of the projection map of the Hopf fibration over the two-sphere. The outcome is the emergence of a five dimensional theory from a three dimensional one as expected from the intersection of the fundamental branes of M-Theory in ABJM quotients of eleven dimensional spacetime. The demonstration of the emergent six dimensional theory expected for the brane intersection in M-Theory without a quotient remains an open problem.