GUT precursors and entwined SUSY: The phenomenology of stable nonsupersymmetric strings

Recent work has established a method of constructing nonsupersymmetric string models that are stable, with near-vanishing one-loop dilaton tadpoles and cosmological constants. This opens up the tantalizing possibility of realizing stable string models whose low-energy limits directly resemble the Standard Model rather than one of its supersymmetric extensions. In this paper we consider the general structure of such strings and find that they share two important phenomenological properties. The first is a so-called “GUT-precursor” structure in which new GUT-like states appear with masses that can be many orders of magnitude lighter than the scale of gauge coupling unification. These states allow a parametrically large compactification volume, even in weakly coupled heterotic strings, and in certain regions of parameter space can give rise to dramatic collider signatures which serve as “smoking guns” for this overall string framework. The second is a residual “entwined-SUSY” (or $e$-SUSY) structure for the matter multiplets in which different multiplet components carry different horizontal $U(1)$ charges. As a concrete example and existence proof of these features, we present a heterotic string model that contains the fundamental building blocks of the Standard Model such as the Standard-Model gauge group, complete chiral generations, and Higgs fields—all without supersymmetry. Even though massless gravitinos and gauginos are absent from the spectrum, we confirm that this model has an exponentially suppressed one-loop dilaton tadpole and displays both the GUT-precursor and $e$-SUSY structures. We also discuss some general phenomenological properties of $e$-SUSY, such as cancellations in radiative corrections to scalar masses, the possible existence of a corresponding approximate moduli space, and the prevention of rapid proton decay.

Figure 1

The spectrum of a generic metastable interpolating model for $R\gg M_s^{-1}$. States with masses below $M_s$ (i.e., below $n=1$) consist of massless observable states, massless hidden-sector states, their would-be superpartners, and their lightest KK excitations. For these lightest states, the net (bosonic minus fermionic) numbers of degrees of freedom from the hidden sector are exactly equal and opposite, level by level, to those from the observable sector. This is true for all large compactification radii. Note that this cancellation of net physical-state degeneracies between the observable and hidden sectors bears no connection with any supersymmetry, either exact or approximate, in the string spectrum. For the heavier states, by contrast, the observable and hidden sectors need no longer supply equal and opposite numbers of degrees of freedom. The properties of these sectors are nevertheless governed by misaligned-supersymmetry constraints, as a result of which the entire string spectrum continues to satisfy the supertrace relations in Eq. (2.1). These relations maintain the finiteness of the overall string theory, even without spacetime supersymmetry. Figure taken from Ref. [1].