Past exam of the mathematics course of the University of Cambridge 2001 iii Paper 70 3 c i Solution Created 2026-10-03 Updated 2026-10-14
The SU(5) grand unified theory has simply connected space and a connected Standard Model subgroup. More precisely that subgroup is ; the product notation suppresses a finite central quotient. The long exact sequence of homotopy groups of a fibration givesThus stable magnetic monopoles form, whereas this transition does not require walls or strings. The monopole core and mass scales in an SU(5) transition are set by the massive gauge and scalar fields:For order-one couplings, the core size is of order and the mass is of order up to the often substantial factor . These heavy objects are nonrelativistic soon after formation and can survive as stable relics.