Condensates and Singularities in String Theory

TL;DR

This paper derives solutions to the string sigma-model equations with a constant tachyon condensate, explores their properties, and discusses how string corrections might resolve classical singularities like big-bang or crunch scenarios.

Contribution

It provides explicit solutions for critical string theories with condensates and analyzes their implications for singularity resolution in string theory.

Findings

Solutions include models with linearly rising dilaton

Stringy corrections may smooth out certain spacetime singularities

Explicit spectrum analysis using Feigin-Fuks method

Abstract

We derive a class of solutions to the string sigma-model equations for the closed bosonic string. The tachyon field is taken to form a constant condensate and the beta-function equations at one-loop level are solved for the evolution of the metric and the dilaton. The solutions represent critical string theories in arbitrary dimensions. The spectrum of the subclass of models with a linearly rising asymptotic dilaton is found using the Feigin-Fuks method. Certain approximate solutions arising in string field theory are used to illustrate the results explicitly. An argument based on conformal invariance leads to the conjecture that that stringy corrections to at least some singular spacetimes in general relativity result in non-singular metrics. We use the singularities of the big-bang/crunch type appearing in our models to examine this conjecture.