Duality without Supersymmetry: The Case of the SO(16)xSO(16) String

TL;DR

The paper demonstrates a concrete strong/weak coupling duality between nonsupersymmetric, tachyon-free string theories by constructing an interpolating heterotic model that connects the $SO(16)\times SO(16)$ string to the supersymmetric $SO(32)$ theory. It then identifies a corresponding open-string dual via a Type IIB orientifold interpolation, showing that in a tachyon-free regime the massless spectra match and a D1-brane soliton on the open-string side behaves as a fundamental $SO(16)\times SO(16)$ string at strong coupling. The analysis combines perturbative spectra, one-loop cosmological constants, and nonperturbative soliton dynamics to argue for a first example of duality between nonsupersymmetric tachyon-free strings and outlines a phase structure where the strongly coupled theory may flow to $E_8\times E_8$ or M-theory. These results illuminate nonperturbative stability and possible endpoint theories for nonsupersymmetric string constructions, with implications for the landscape of consistent string vacua.

Abstract

We extend strong/weak coupling duality to string theories without spacetime supersymmetry, and focus on the case of the unique ten-dimensional, nonsupersymmetric, tachyon-free $SO(16)\times SO(16)$ heterotic string. We construct a tachyon-free heterotic string model that interpolates smoothly between this string and the ten-dimensional supersymmetric $SO(32)$ heterotic string, and we construct a dual for this interpolating model. We find that the perturbative massless states of our dual theories precisely match within a certain range of the interpolation. Further evidence for this proposed duality comes from a calculation of the one-loop cosmological constant in both theories, as well as the presence of a soliton in the dual theory. This is therefore the first known duality relation between nonsupersymmetric tachyon-free string theories. Using this duality, we then investigate the perturbative and nonperturbative stability of the $SO(16)\times SO(16)$ string, and present a conjecture concerning its ultimate fate.

Figures (3)

• Figure 1: The one-loop cosmological constants $\Lambda^{(9)}$ (left plot) and $\tilde{\Lambda}$ (right plot) as functions of the radius $R_H$ of the compactified dimension, in units of ${{1\over 2}}{\cal M}^{9}$ and ${{1\over 2}}{\cal M}^{10}$ respectively. This model reproduces the supersymmetric $SO(32)$ heterotic string as $R_H\to \infty$ and the nonsupersymmetric $SO(16)\times SO(16)$ heterotic string as $R_H\to 0$.
• Figure 2: The total one-loop cosmological constant $\tilde{\Lambda}$ for our open-string interpolating model, plotted in units of ${{1\over 2}} {\cal M}^{10}$, as a function of the radius $R_I$ of the compactified dimension. Also shown (dashed lines) are the separate torus and Möbius-strip contributions; note that the Klein-bottle and cylinder contributions vanish. This open-string model reproduces the supersymmetric $SO(32)$ Type I string as $R_I\to \infty$, and has gauge group $SO(16)\times SO(16)$ for all finite radii. The torus amplitude develops a divergence below $R^\ast/\sqrt{\alpha'}\equiv 2\sqrt{2}\approx 2.83$, which reflects the appearance of a tachyon in the torus amplitude below this radius. All other contributions are tachyon-free for all radii.
• Figure 3: The proposed phase diagram for the $SO(16)\times SO(16)$ interpolating model. For $\lambda_H^{(10)} < R_H^2 / (R^\ast)^2$, the theory is in Phase I and flows to the ten-dimensional weakly coupled heterotic supersymmetric $SO(32)$ theory. For $\lambda_H^{(10)} > R_H^2 / (R^\ast)^2$, by contrast, the theory is expected to flow to the ten-dimensional strongly coupled supersymmetric $E_8\times E_8$ string. On the boundary, the theory is stable against passing into Phase I. The dotted lines are contours of constant $T$-dual coupling $\lambda_H^\prime \equiv \sqrt{\alpha'}\lambda_H^{(10)}/R_H$.