Singularities in string theory

Abstract

String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework for geometry that reduces to ordinary differential geometry when the curvature is asymptotically small. In the 1990's, many interesting results were obtained about the behavior of string theory in spacetimes that develop singularities. In many cases, the physics at the singularity is governed by an effective Lagrangian constructed using an interesting bit of classical geometry such as the association of A-D-E groups with certain hypersurface singularities or the ADHM construction of instantons. In other examples, the physics at the singularity cannot be described in classical terms but involves a non-Gaussian conformal field theory.

Cited by in corpus (10)

• Solvable models of strings in homogeneous plane wave backgrounds
• Dynamical behavior near explicit self-similar blow up solutions for the Born-Infeld equation
• More on the regularized big bang singularity
• Nonsingular bouncing cosmology from general relativity: Scalar metric perturbations
• Asymptotics of flat, radiation universes in quadratic gravity
• Explicit self-similiar singularity of Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation
• Hilbert-Kunz functions of surface rings of type ADE
• A new track for unifying general relativity with quantum field theories
• Global stability dynamics of the timelike extremal hypersurfaces in Minkowski space
• Nonlinear stability of explicit self-similar solutions for the timelike extremal hypersurfaces in R^{1+3}