Toroidal Compactification in String Theory from Chern-Simons 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.

arXiv comment32+2 pages, 9 figures. Comments added and minor changes in section 3. Content not altered

References in corpus (12)

• The World as a Hologram
• Target Space Duality in String Theory
• Spontaneous Symmetry Breaking at Two Loop in 3-d Massless Scalar Electrodynamics
• Compact QED${}_3$ - a simple example of a variational calculation in a gauge theory
• Conformal Dimensions from Topologically Massive Quantum Field Theory
• Boundary Conditions and Heterotic Construction in Topological Membrane Theory
• Chern-Simons States and Topologically Massive Gauge Theories
• Mirror Maps in Chern-Simons Gauge Theory
• String Winding Modes From Charge Non-Conservation in Compact Chern-Simons Theory
• Quantum Liouville Theory from a Diffeomorphism Chern-Simons Action
• Induced Dilaton in Topologically Massive Quantum Field Theory
• Liouville Dressed Weights and Renormalization of Spin in Topologically Massive Gravity

Cited by in corpus (5)

• D-branes in Massive IIA and Solitons in Chern-Simons Theory
• Searching for a Connection Between Matroid Theory and String Theory
• Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory
• U_e(1)xU_g(1) Actions in 2+1-Dimensions: Full Vectorial Electric and Magnetic Fields
• D-Branes in Topological Membranes