Grand Unified Theories Sample Clauses

Grand Unified Theories. ‌ Another fundamental building block of particle physics beyond the Standard Model are Grand Unified Theories, or GUTs. In this section, we discuss their relevance and some of their properties relevant to this thesis. Much more can be said about GUTs, and an introductory review is [36]. For Lie groups and Lie algebras, we use notation as presented in [37, 38]. The central observation underlying the idea of GUTs [39, 40] is that the Standard Model gauge group GSM from (1.1.1) is a maximal subgroup of SU (5). That is, there exists exactly one element up to scaling in su(5), the Lie algebra of SU (5), which commutes with the su(3) ⊕ su(2) subalgebra of su(5). This element generates the U (1)Y in GSM. The decomposition of the adjoint 24 representation of SU (5), in which the SU (5) gauge bosons transform, is given by 24 → (8, 1)0 + (1, 3)0 + (1, 1)0 + 3, 2 −5 + 3, 2 5 . (1.3.1) The first three terms are precisely the required gauge bosons of SU (3), SU (2), and U (1) of GSM, respectively. The last two terms however do not appear in the Standard Model spectrum. The gauge bosons to which these representations correspond to are typically denoted X- and Y -bosons. The existence of such bosons at the electroweak scale would induce proton decay at a magnitude that has been experimentally ruled out. In fact, the mass of X and Y bosons has to be roughly at the GUT scale of 1016 GeV. Furthermore, decomposing the antifundamental 5 and antisymmetric 10 representations of SU (5) in terms of representations of SU (3) × SU (2) × U (1), one finds 5 → 3, 1 2 + 1, 2 −3 , 10 → (3, 2)1 + 3, 1 −4 + (1, 1)6 .