N=2 extended supersymmetric GUTs

Abstract

Abstract We construct N =2 extended SUSY GUTs which provide a general association between massive spin-1 gauge bosons, spin - 1 2 inos and spin-0 Higgs bosons. The corresponding gauge hypermultiplets are of four different types: 1. (i) massless the photon, 2 Majorana photinos and 2 real spin-0 photons the gluons, 2 octet Majorana gluinos and 2 real octet spin-0 gluons 2. (ii) massive type I: e.g. the W ± , 4 Dirac winos and 5 charged Higgs bosons the Z, 4 Dirac winos and 5 neutral Higgs bosons 3. (iii) massive type II: e.g. the X ± 4 3 , 2 Dirac xinos and 1 charged triplet Higgs boson; 4. (iv) massive type III: e.g. the Y ± 1 3 , 4 Dirac yinos and 5 charged triplet Higgs bosons; while leptons and quarks are associated with mirror and spin-0 partners. The anticommutators of the two supersymmetry generators provide two spin-0 symmetry generators Z s and Z p , which do not commute. Their field-independent parts 〈 Z s 〉 and 〈 Z p rang; do commute, however, and appear as central charges in the symmetry algebra of the spontaneously broken gauge theory . These central charges 〈 Z s 〉 and 〈 Z p 〉 are linear combinations of global symmetry generators with grand unification generators such as the weak hypercharge (but not the electrical charge!). They survive the electroweak symmetry breaking. They do not vanish for massive gauge hypermultiplets of types II and III, which verify M 2 =〈Z s 〉 2 +〈Z p 〉 2 >0 and M 2 >〈Z s 〉 2 +〈Z p 〉 2 >0 , respectively. The formula M 2 ≅〈Z s 〉 2 +〈Z p 〉 2 determines the mass spectrum on the grand unification scale, up to electroweak corrections. Finally, we indicate how our mass relations can be interpreted in a 5- or 6-dimensional formalism, the central charges appearing as the extra components of the covariant momentum along the compact fifth or sixth dimensions; and how to evaluate the grand unification mass m x in terms of the lengths of the latter ( m x ∼ℏ/ L 5(6) c ).