Brane solutions in strings with broken supersymmetry and dilaton tadpoles

TL;DR

The paper analyzes dilaton-tadpole effects in ten-dimensional nonsupersymmetric tachyon-free strings, focusing on the USp(32) Type I and SO(16)×SO(16) heterotic theories. By solving the low-energy Einstein–dilaton equations under maximally symmetric ansätze, it obtains static backgrounds with nine-dimensional Poincaré symmetry in which the tenth dimension is dynamically compact and the effective $M_P^7$ and $1/g_{YM}^2$ are finite, hinting at a spontaneous 9D compactification. It also presents a cosmological-type solution with big-bang–like singularities. The work highlights the role of NS-NS tadpoles in shaping viable backgrounds and discusses caveats related to singularities and quantum corrections, leaving open questions on stability and the full consistency of these vacua.

Abstract

The tachyon-free nonsupersymmetric string theories in ten dimensions have dilaton tadpoles which forbid a Minkowski vacuum. We determine the maximally symmetric backgrounds for the $USp(32)$ Type I string and the $SO(16)\times SO(16)$ heterotic string. The static solutions exhibit nine dimensional Poincaré symmetry and have finite 9D Planck and Yang-Mills constants. The low energy geometry is given by a ten dimensional manifold with two boundaries separated by a finite distance which suggests a spontaneous compactification of the ten dimensional string theory.