Abstract

We show that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world-volume theories. This gives strong evidence that they are well-defined quantum theories. It also gives a physical derivation of the identification proposed by Connes, Douglas and Schwarz of Matrix theory compactification on the noncommutative torus with M theory compactification with constant background three-form tensor field. November 1997It is often stated that in toroidal compactification in superstring theory, there is a minimum radius for the torus, the string length. Tori with smaller radii can always be related to tori with larger radii by using T-duality. However, this picture is not correct in the presence of other background fields, as is clear from the following simple example. Consider compactification on T 2 with a constant Neveu-Schwarz two-form field B. We quote the standard result [1]: under simultaneous T-duality of all coordinates, the combination (G + B)ij is inverted, where G is the metric expressed in string units. Consider a square torus and take the limit R1 = R2 → 0; B ̸ = 0 fixed. (1) The T-dual torus has G + B =