Moduli Space of Standard Model

Question

I have been discussing with a couple of colleagues about this issue and do not come to an agreement. 

1. Is the Moduli Space of the Standard model a circle or a point? It may appear to be a circle, but one can argue that the circle is coming form a gauge symmetry which is not physical, so it is modded out. 

2. A related question is: is there a massless scalar in the standard model (It being "eaten " is just an artefact of unitary gauge) or is it fundamentally eaten, and so unphysical (Can't be measured but as a part of the fat gauge boson, any correlator with only this massles guy is not Lorentz Invariant).  

(Copied from StackExchange)

Comments

could you help please with some precisions : what moduli space exactly ? Is it not commonly the one of the Dirac operators which has a set of coordinates that can never be reduced to 1 element ?

---

I am afraid I can´t follow the comment. In any case I meant the space spanned by vev's of masless scalar fields. 

---

it was not a comment but a request of precision ... In fact, in my books the moduli space of the SM is something different that cannot be related to a point ( nor a circle ). A simple ref would be welcome. Thanks.

---

I do not really have a ref, although I have looked for one. But would really appreciate if you gave me yours! 

Thanks

---

there are from Alain Connes in french. You have almost the same with Matilde Marcolli , The Spectral Geometry of the Standard Model ( pdf )

Answer 1

The moduli space of the Standard Model is a point.

There is no massless scalar in the Standard Model.

Comments

Thanks!