String winding modes from charge non-conservation in compact Chern-Simons theory

In this letter we show how string winding modes can be constructed using topological membranes. We use the fact that monopole-instantons in compact topologically massive gauge theory lead to charge non-conservation inside the membrane which, in turn, enables us to construct string vertex operators with different left and right momenta. The amount of charge non-conservation inside the membrane is interpreted as giving the momentum associated with the string winding mode and is shown to match precisely the full mass spectrum of compactified string theory. We also argue that if heterotic strings are described by topological membranes, then all space-time dimensions must be compact.