Non-commutative geometry from 0-branes in a background B-field Original Research Article

We study 0-branes in type IIA on T2 with a background B-field turned on. This enables us to find the matrix model for M-theory on T2 with a background 3-form potential along the torus and the lightlike circle. The theory is a non-local (2 + 1)-dimensional SYM theory on a dual T2 exactly as proposed by Connes, Douglas and Schwarz. We calculate the radii and the gauge coupling for the SYM on the dual T2 for all choices of longitudinal momentum and membrane wrapping number on the T2.