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, selfdual 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.

Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory

“…An unsolved problem that remains concerns the construction of more general modular invariants. Within the present framework this is is not possible without a mechanism which creates a tunnelling effect between various ground state wavefunctions that is more general than the one described in [32]. For this, it is most likely necessary to take into account the effects of gravity in the bulk theory [22,35,60].…”

“…The wavefunctions of topologically massive gauge theory [58], inserted at each of the boundaries, work as chiral WZNW models [44] and render the theory well-defined by effectively enforcing the appropriate boundary conditions on the full three-dimensional gauge theory [34,38]. One also has to consider the monopole effects described in [32] in order to get the correct holomorphic-antiholomorphic pairing of the chiral conformal blocks. However, these boundary insertions must be suitably modified, because we want to orbifold the bulk theory, but the wavefunctions only live at the boundaries.…”

“…The electric charge spectrum of the quantum field theory is [25] Q m,n = m + k 4 n , (2.16) where m and n are integers representing, respectively, the contributions from the usual Dirac charge quantization and the monopole flux. Due to the existence of monopole induced processes and linkings between Wilson lines (charge trajectories) it can be shown [32] that, with the correct relative boundary conditions, the insertion of the charge Q m,n at one boundary Σ 0 (corresponding to a vertex operator insertion in the boundary conformal field theory) necessitates an insertion of the chargē…”

“…Notice that the fields ϕ living on Σ 0 correspond to holomorphic degrees of freedom while the ones living on Σ 1 correspond to antiholomorphic degrees of freedom. This method of constructing the two chiral conformal field theories on the boundary is thereby equivalent to that described in [23,32] (see also [34,44]) by fixing the fields on the boundary and adding extra terms to the boundary action.…”

D-branes in Massive IIA and Solitons in Chern-Simons Theory

“…For other occurences of Chern-Simons theory in string theory see [12][13] [14]. Massive IIA has a positive cosmological constant proportional to (F (0) ) 2 , the dual of the ten form field strength that couples to the D8-brane, and a linear dilaton potential.…”