Strings and the Gauge Theory of Spacetime Defects

Abstract

we present a new topological invariant to describe the space-time defect which is closely related to torsion tensor in Riemann-Cartan manifold. By virtue of the topological current theory and $ϕ$-mapping method, we show that there must exist many strings objects generated from the zero points of $ϕ$-mapping, and these strings are topological quantized and the topological quantum numbers is the Winding numbers described by the Hopf indices and the Brouwer degrees of the $ϕ$-mapping.