Strings in Singular Space-Times and their Universal Gauge Theory

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 $\mathcal{F}$ 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 $\mathcal{F}$ 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 $TM\oplus T^{\ast }M$.

49 pages, 4 figures

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• Homotopy momentum sections on multisymplectic manifolds
• Topological Dirac Sigma Models and the Classical Master Equation
• Duality, generalized global symmetries and jet space isometries
• Basic curvature and the Atiyah cocycle in gauge theory
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example