Toroidal Compactification in String Theory from Chern-Simons Theory

TL;DR

This paper explores how three-dimensional topological gauge theories can naturally produce the charge spectra and compactification constraints of string theory, linking boundary CFTs to string sectors and deriving RCFT structures.

Contribution

It demonstrates that Narain compactification constraints and RCFT structures can be derived from three-dimensional topological gauge theories, providing a new perspective on string compactification.

Findings

Narain constraints have a natural interpretation in 3D gauge theory.

Boundary CFTs correspond to string sectors in the topological membrane approach.

Derived the block structure of c=1 RCFT from gauge theory.

Abstract

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.