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

TL;DR

This paper constructs explicit strong/weak coupling dualities for non-supersymmetric, tachyon-free string theories, demonstrating their non-perturbative stability and connecting them to supersymmetric models through interpolating constructions.

Contribution

It introduces the first known strong-coupling duals for non-supersymmetric, tachyon-free heterotic strings using heterotic and open-string interpolations.

Findings

Non-supersymmetric dual theories share the same massless spectra within certain ranges.

Solitons in dual theories match heterotic counterparts, confirming duality.

Proposed phase diagram illustrates string behavior across coupling and radius.

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.