Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-10-16
JHEP 0212 (2002) 005
Physics
High Energy Physics
High Energy Physics - Theory
17 pp, 2 figs, plain tex. v2: refs. added
Scientific paper
10.1088/1126-6708/2002/12/005
We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the coordinates obeying Dirichlet boundary conditions. A linear term acts as an outer derivation on the subalgebra of volume-preserving diffeomorphisms generated by single-valued functions, and obstructs the truncation to matrix theory obtained via non-commutativity with rational parameter. As long as only one of the two membrane directions is stretched, the possible consistent truncation is to coordinates taking values in representations of an affine algebra. We show that this consistent truncation of the supermembrane gives a precise microscopic derivation of matrix string theory with the representation content appropriate for the physical situation. The matrix superstring theory describing parallel M5-branes is derived. We comment on the possible applications of the construction to membrane quantisation in certain M-theory backgrounds.
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