# Massless excitations without SSB

Is there a possible situation where there are massless excitations in spectrum of states in a theory with phase transition but without spontaneous symmetry breaking?

The motivation for this question is Elitzur's theorem which forbids SSB of gauge symmetries. If I understand correctly, this provides the statement that there is no SSB of electroweak gauge symmetry group (rather physical states don't form irreps of gauge group below the scale at which Higgs double ). Hence existence of massless unphysical (which can be absorbed by gauge bosons fields) states isn't due to SSB.

• Any system with a second order phase transition has massless excitations at the critical point, even if there are no Goldstone modes in the phase with broken symmetry. – TotallyRhombus May 12 '16 at 5:36
• @fs137 :but what if there is no SSB,but there is the crossover (like in SM)? – Name YYY May 12 '16 at 9:56
• I had quantum critical points in mind, but I imagine there's some way of looking at crossover phenomena in the standard model that would allow special massless states to be defined at the 'transition point' (say, where electroweak symmetry breaks in some thermal slowly evolving effective field theory). I'd also imagine that these states are somewhat contrived though. – TotallyRhombus May 12 '16 at 19:05
• @fs137 : so, You say that there is phase transition in SM, and there are corresponding massless excitations, don't You? If yes, what is the reason of their appearance (in general)? Could You give some link or briefly explain, if You please? – Name YYY May 14 '16 at 12:34