Folded Strings

TL;DR

This paper reviews solutions of two-dimensional classical string theory in curved spacetime, highlighting new behaviors at singularities like black holes and proposing a mathematical framework involving recursion relations.

Contribution

It introduces a new mathematical structure using recursion relations to describe folded string solutions in curved spacetime, especially near singularities.

Findings

Deformed folded string solutions in smooth curvature

New stringy behaviors at black hole singularities

Inclusion of the 'bare singularity region' in global solutions

Abstract

Recent progress on the complete set of solutions of two dimensional classical string theory in any curved spacetime is reviewed. When the curvature is smooth the string solutions are deformed folded string solutions as compared to flat spacetime folded strings that were known for 19 years. However, surprizing new stringy behavior becomes evident at singularities such as black holes. The global properties of these solutions require that the ``bare singularity region"of the black hole be included along with the usual black hole spacetime. The mathematical structure needed to describe the solutions include a recursion relation that is analogous to the transfer matrix of lattice theories. This encodes lattice properties on the worldsheet on the one hand and the geometry of spacetime on the other hand. A case is made for the presence of folded strings in the quantum theory of non-critical strings for $d\geq 2$.