Strings below the Planck scale

TL;DR

This paper investigates the behavior of a class of critical strings in a specific target space, revealing a breakdown of the analog model description below a certain radius and identifying a soft singularity at the self-dual point.

Contribution

It demonstrates the failure of the field content-based description of string theory below the self-dual radius in a specific target space, highlighting a soft singularity in the partition function.

Findings

The analog model breaks down below the self-dual radius R0.

Partition function Z(R) exhibits a soft singularity at R0.

A finite jump in the first derivative of Z(R) occurs at R0.

Abstract

We show that, for a class of critical strings in ${\bf R}\times S^{1}$-target space, the description of string theory given by its field content (analog model) breaks down when the radius of $S^{1}$ decreases below $R_{0}=\sqrt{\alpha^{\prime}}$, the self-dual point of the partition function $Z(R)$. We find that $Z(R)$ has a soft singularity at $R_{0}$ (a finite jump in the first derivative of $Z$).