Global Symmetry Breaking:- A perspective on Symmetry Inconsistencies

Global Symmetries are inconsistent with Quantum Gravity. Most global symmetries are broken/gauged away at lower energies . These kind of symmetries, even though are derived well out of Quantum Field Theories and General Relativity, it undergoes spontaneous symmetry breaking at low energy levels and remain lacking at unification. Spontaneous Symmetry Breaking(SSB) gives rise to Goldstone modes which signals the presence of massless excitations. A great example of SSB is the Higgs Field. The problem has been approached from a few different perspectives- namely - global symmetries on the string worldsheet, the consequences of symmetry breaking that happens on a conserved Noether's charge and how divergences occur when the vacuum state does not remain invariant and finally a topological perspective to how gauge symmetry is broken and how it leads to the rise of both broken and unbroken generators and mass terms.

Major focus has been devoted towards understanding how a non-triviality approach in the context of conserved Noether current as well as a Holonomy group can give us deep insight on how divergences lead to inconsistencies(this is very apparent in case of Black Holes). It also provides information as to how compactification of higher dimensional gauge group leads to the breakdown of gauge symmetry.