String Theory and the Path to Unification: A Review of Recent Developments

TL;DR

<3-5 sentence high-level summary>Gauge coupling unification in string theory faces a mismatch between the MSSM-scale unification and the string-scale unification tied to gravity. The paper surveys seven unification pathways—string GUTs, non-standard affine levels, heavy and light thresholds, intermediate-scale matter, and non-perturbative or non-supersymmetric scenarios—and assesses their viability with realistic, three-generation string models. It finds heavy thresholds and light thresholds generally insufficient to reconcile scales in current models, while extra non-MSSM matter often offers the most plausible route, albeit with model-dependent mass scales and spectrum constraints. The work highlights the interconnectedness of worldsheet symmetries, moduli, and spectrum in determining viable unification, and points to a need for hybrid approaches and further non-perturbative insights to realize a fully realistic string-based unification.

Abstract

This is a pedagogical review article surveying the various approaches towards understanding gauge coupling unification within string theory. As is well known, one of the major problems confronting string phenomenology has been an apparent discrepancy between the scale of gauge coupling unification predicted within string theory, and the unification scale expected within the framework of the Minimal Supersymmetric Standard Model (MSSM). In this article, I provide an overview of the different approaches that have been taken in recent years towards reconciling these two scales, and outline some of the major recent developments in each. These approaches include 1) string GUT models; 2) higher affine levels and non-standard hypercharge normalizations; 3) heavy string threshold corrections; 4) light supersymmetric thresholds; 5) effects from intermediate-scale gauge and matter structure beyond the MSSM; 6) strings without supersymmetry; and 7) strings at strong coupling.

Figures (12)

• Figure 1: One-loop evolution of the gauge couplings within the (non-supersymmetric) Standard Model. Here $\alpha_1\equiv (5/3)\alpha_Y$, where $\alpha_Y$ is the hypercharge coupling in the conventional normalization. The relative width of each line reflects current experimental uncertainties.
• Figure 3: The fundamental problem of gauge coupling unification within string theory: the scale $M_1\equiv M_{\rm MSSM}\approx 2\times 10^{16}$ GeV at which the gauge couplings are expected to unify within the MSSM is significantly below the scale $M_2\equiv M_{\rm string}\approx 5\times 10^{17}$ GeV at which string theory predicts their unification with each other and with the gravitational coupling (Newton constant) $G_N$.
• Figure 4: Dependence on the string scale: the predicted value of the low-energy electroweak mixing angle $\sin^2\theta_W(M_Z)$, assuming unification at $M_{\rm string}$. Results for both one-loop and two-loop running are plotted.
• Figure 6: Various paths to unification, as discussed in the text. Each path provides a different solution to the fundamental problem posed in Fig. \ref{['couplings1']}.
• Figure 7: The root system of $SU(2)_1^{(A)}\times SU(2)_1^{(B)}$ (denoted by open circles), and its dimensional truncation onto the diagonal subgroup $SU(2)_2^{(V)}$ (with new non-zero roots denoted by shaded circles).