Toroidal compactification in string theory from Chern-Simons theory

A detailed study of the charge spectrum of three-dimensional Abelian Topolo gical Massive Gauge Theory (TMGT) is given. When this theory is defined on a manifold with two disconnected boundaries there are induced chiral Confor mal Field Theories (CFT's) on the boundaries which can be interpreted as th e left and right sectors of closed strings. We show that Narain constraints on toroidal compactification (integer, even, self-dual momentum lattice) h ave a natural interpretation in purely three-dimensional terms. This is an important result which is necessary to construct toroidal compactification and heterotic string from Topological Membrane (TM) approach to string theo ry. We also derive the block structure of c = 1 Rational Conformal Field Th eory (RCFT) from the three-dimensional gauge theory. (C) 2000 Elsevier Scie nce B.V. All rights reserved.