Strings below the Planck scale

Abstract

We show that, for a class of critical strings in $\mathbf{R}\times S^1$-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 $Z$).

8 pages

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