Strings in Singular Space-Times and their Universal Gauge Theory

TL;DR

This paper develops a gauge theory framework for bosonic string propagation in singular space-times modeled as quotients of smooth manifolds by singular foliations, without restricting to group actions.

Contribution

It introduces a universal gauge theory approach using the generalized tangent bundle to describe strings in singular target spaces, broadening previous methods.

Findings

Proposes a smooth functional ensuring string propagation in singular spaces.

Shows gauging can be achieved by a universal gauge theory on the generalized tangent bundle.

Does not require the foliation to be generated by a group action.

Abstract

We study the propagation of bosonic strings in singular target space-times. For describing this, we assume this target space to be the quotient of a smooth manifold $M$ by a singular foliation ${\cal F}$ on it. Using the technical tool of a gauge theory, we propose a smooth functional for this scenario, such that the propagation is assured to lie in the singular target on-shell, i.e. only after taking into account the gauge invariant content of the theory. One of the main new aspects of our approach is that we do not limit ${\cal F}$ to be generated by a group action. We will show that, whenever it exists, the above gauging is effectuated by a single geometrical and universal gauge theory, whose target space is the generalized tangent bundle $TM\oplus T^*M$.