Grand Unified Theories From Superstrings

I review how traditional grand unified theories, which require adjoint (or higher representation) Higgs fields for breaking to the standard model, can be contained within string theory. The status (as of January 1996) of the search for stringy free fermionic three generation SO(10) SUSY–GUT models is discussed. Progress in free fermionic classification of both SO(10)2 charged and uncharged embeddings and in N = 1 spacetime solutions is presented. Based on talks presented at the Workshop on SUSY Phenomena and SUSY GUTs, Santa Barbara, California, Dec. 7-11, 1995, and at the Orbis Scientiae, Coral Gables, Florida, January 25-28, 1996. To appear in the Proceedings of Orbis Scientiae, 1996. ∗E-mail address: [email protected] SUSY–GUTs and Strings Elementary particle physics has achieved phenomenal success in recent decades, resulting in the Standard Model (SM), SU(3)C×SU(2)L×U(1)Y, and verification to high precision of many SM predictions. However, many aspects of the SM point to a more fundamental, underlying theory: • the SM is very complicated, requiring measurement of some 19 free parameters, • the SM has a complicated gauge structure, • there is a naturalness problem regarding the scale of electroweak breaking, • fine-tuning is required for the strong CP problem, and • the expected cosmological constant resulting from electroweak breaking is many, many orders of magnitude higher than the experimental limit. Since the early 1980’s, these issues have motivated investigation of Grand Unified Theories (GUTs) that would unite SM physics through a single force at higher temperatures. Superstring research[1] has attempted to proceed one step further and even merge SM physics with gravity into a “Theory of Everything.” Perhaps the most striking evidence for a symmetry beyond the SM is the predicted coupling unification not for the SM, but for the minimal supersymmetric standard model (MSSM) containing two Higgs doublets.[2] Renormalization group equations applied to the SM couplings measured around the MZ0 scale predict MSSM unification at Munif ≈ 2.5 × 10 16 GeV. However, this naively poses a problem for string theory, since the string unification scale has been computed, at tree level, to be one order of magnitude higher. That is, Mstring ≈ gs × 5.5 × 10 17 GeV, where the string coupling gs ≈ 0.7.[3] In recent years, three classes of solutions have been proposed to resolve the potential inconsistency between Munif and Mstring:[4] • The unification of the MSSM couplings at 2.5× 10 GeV should be regarded as a coincidence. Munif could actually be higher as a result of 1. SUSY–breaking thresholds,[8] 2. non–MSSM states between 1TeV and Munif ,[5] 3. non–standard hypercharge normalization (a stringy effect),[6, 18] or 4. non-perturbative effects.[7] • Mstring could be lowered by string threshold effects,[3] or • Munif and Mstring remain distinct: there is an effective GUT theory between the two scales. MSSM couplings unify around 10 GeV and run with a common value to the string scale.