Topological Background Fields as Quantum Degrees of Freedom of Compactified Strings

TL;DR

This paper demonstrates that topological background fields in compactified string theories act as quantum degrees of freedom related to zero mode representations, which are not fixed by nonperturbative string dynamics.

Contribution

It reveals that topological background fields correspond to quantum degrees of freedom associated with zero mode algebra representations in compactified strings.

Findings

Topological background fields are linked to quantum degrees of freedom.

These degrees of freedom are parametrized by choices of zero mode representations.

Their values cannot be determined by nonperturbative string dynamics.

Abstract

It is shown that background fields of a topological character usually introduced as such in compactified string theories correspond to quantum degrees of freedom which parametrise the freedom in choosing a representation of the zero mode quantum algebra in the presence of non-trivial topology. One consequence would appear to be that the values of such quantum degrees of freedom, in other words of the associated topological background fields, cannot be determined by the nonperturbative string dynamics.