Strong/Weak Coupling Duality Relations for Non-Supersymmetric String Theories

Abstract

Both the supersymmetric $SO(32)$ and $E_8\times E_8$ heterotic strings in ten dimensions have known strong-coupling duals. However, it has not been known whether there also exist strong-coupling duals for the non-supersymmetric heterotic strings in ten dimensions. In this paper, we construct explicit open-string duals for the circle-compactifications of several of these non-supersymmetric theories, among them the tachyon-free $SO(16)\times SO(16)$ string. Our method involves the construction of heterotic and open-string interpolating models that continuously connect non-supersymmetric strings to supersymmetric strings. We find that our non-supersymmetric dual theories have exactly the same massless spectra as their heterotic counterparts within a certain range of our interpolations. We also develop a novel method for analyzing the solitons of non-supersymmetric open-string theories, and find that the solitons of our dual theories also agree with their heterotic counterparts. These are therefore the first known examples of strong/weak coupling duality relations between non-supersymmetric, tachyon-free string theories. Finally, the existence of these strong-coupling duals allows us to examine the non-perturbative stability of these strings, and we propose a phase diagram for the behavior of these strings as a function of coupling and radius.

Figures (14)

• Figure 1: The relation between the seven non-supersymmetric heterotic string models in ten dimensions and the supersymmetric $SO(32)$ and $E_8\times E_8$ string models. Each arrow indicates a ${ Z Z}_2$ orbifold relation that breaks spacetime supersymmetry. Only the tachyon-free $SO(16)\times SO(16)$ string can be realized as a ${ Z Z}_2$ orbifold of both the supersymmetric $SO(32)$ string and the $E_8\times E_8$ string.
• Figure 2: Proposed method for deriving the dual of the heterotic $SO(16)\times SO(16)$ string model through continuous deformations away from the supersymmetric $SO(32)$ string model. Analogous deformations exist on both the heterotic and the Type II sides, from which corresponding Type I deformations can be obtained through orientifolding.
• Figure 3: Alternating boson/fermion surpluses in the $D=10$ non-supersymmetric tachyon-free $SO(16)\times SO(16)$ heterotic string. For each mass level $\alpha' M_2\in 2{ Z Z}$ in this model, we plot $\pm \log_{10}(|B_M-F_M|)$ where $B_M$ and $F_M$ are respectively the numbers of spacetime bosonic and fermionic states at that level. The overall sign is chosen positive if $B_M>F_M$, and negative otherwise. The points are connected in order to stress the alternating, oscillatory behavior of the boson and fermion surpluses throughout the string spectrum. These oscillations insure that ${{\rm Str}\,} M^0= {{\rm Str}\,} M^2= {{\rm Str}\,} M^4= {{\rm Str}\,} M^6=0$ in this model, even though there is no spacetime supersymmetry.
• Figure 4: Several ${ Z Z}_2$ orbifold connections between ten-dimensional heterotic string models, as discussed in the text. Note the highly symmetric position of the tachyon-free $SO(16)\times SO(16)$ model.
• Figure 5: Nine-dimensional Models A through D interpolate between different supersymmetric and non-supersymmetric ten-dimensional string models. In each case, supersymmetry is restored in one limit only. Model E interpolates between the supersymmetric $SO(32)$ and $E_8\times E_8$ models, and is therefore supersymmetric at all radii.