Noncommutative Geometry from D0-branes in a Background B-field

Details Noncommutative Geometry from D0-branes in a Background B-field Noncommutative Geometry from D0-branes in a Background B-field

1998-03-04

arxiv.org/abs/hep-th/9803031v2

Nucl.Phys. B528 (1998) 185-196

Physics

High Energy Physics

High Energy Physics - Theory

13pp, harvmac with five eps figures; final version in Nuclear Physics B

Scientific paper

10.1016/S0550-3213(98)00380-0

We study D0-branes in type IIA on $T^2$ with a background B-field turned on. We calculate explicitly how the background B-field modifies the D0-brane action. The effect of the B-field is to replace ordinary multiplication with a noncommutative product. This enables us to find the matrix model for M-theory on $T^2$ with a background 3-form potential along the torus and the lightlike circle. This matrix model is exactly the non-local 2+1 dim SYM theory on a dual $T^2$ proposed by Connes, Douglas and Schwarz. We calculate the radii and the gauge coupling for the SYM on the dual $T^2$ for all choices of longitudinal momentum and membrane wrapping number on the $T^2$.

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