Toroidal Compactification in String Theory from Chern-Simons Theory

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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32+2 pages, 9 figures. Comments added and minor changes in section 3. Content not altered

Scientific paper

10.1016/S0550-3213(00)00407-7

A detailed study of the charge spectrum of three dimensional Abelian Topological Massive Gauge Theory (TMGT) is given. When this theory is defined on a manifold with two disconnected boundaries there are induced chiral Conformal Field Theories (CFT's) on the boundaries which can be interpreted as the left and right sectors of closed strings. We show that Narain constraints on toroidal compactification (integer, even, self-dual momentum lattice) have 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 theory. We also derive the block structure of $c=1$ Rational Conformal Field Theory (RCFT) from the three dimensional gauge theory.

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