# Does Goldstone theorem have anything to do with Cosmic string

Cosmic strings are formed due to topological defects during symmetry breaking phase transition in early universe.

While Goldstone theorem states whenever we have continuous symmetry and it is spontaneously broken then we have scalar particles appearing in spectrum of excitation.

I'm wondering if these concept have any correlation? Also as I have marked we should have a spontaneous symmetry breaking for Goldstone theorem to hold but wiki article doesn't state whether cosmic strings have to be formed during spontaneous symmetry breaking.

• When you look around, defects appear to be the hallmark of spontaneous symmetry breaking. I don't know if this can be rigorously formalized.
– SRS
Jul 6, 2020 at 2:57
• Presumably, Godstone theorem for higher-form symmetries, in this case a one-form symmetry. Check Gaiotto's et al's "Generalized Global Symmetries". They do discuss the generalization of Goldstone to lower dimensional defects. Jul 7, 2020 at 1:53

In short yes.

I believe this idea arose when people were thinking of the symmetry breaking from a bigger symmetry group (for example some hypothetical GUT scale group), down to the standard model as the universe cooled down.

Morally speaking, the same story of the Higgs mechanism applies. That is we have a theory with symmetry group $$G$$ in which the vacuum has isotropy group $$H$$. Your vacuum now lives in $$G/H$$ and defects exists when the first homotopy group $$\pi_1(G/H)$$ is non-trivial. For larger group you have something more complicated than the Higgs model.