Breaking SU(3)xU(1) to SU(2) Exercise: A Search for Solutions

[arivero]

Can anyone provide a pointer to the exercise of higgs breaking SU(3)xSU(2)xU(1) down to SU(2)? I expect it to be solved somewhere in the web...

 

[BenTheMan]

It should be pretty easy. What is it, exactly, that you're interested in?

 

[arivero]

It should be pretty easy. What is it, exactly, that you're interested in?

First, to check I am guessing it right. The Higgs content, etc. And what happens with U(1): do we forcefully get the nonchiral U(1) of electromagnetism, or does it depend of the breaking?

As you say, it is easy and one could expect to find it in some web of solved QFT exercises.

My long shot is to relate the breakings with the compactifications of extra Kaluza Klein dimensions. I would expect Standard Model ---> SU(2) to correspond with a compactification from dimension 10 or 11 to dimension 6.

 

[BenTheMan]

First, to check I am guessing it right. The Higgs content, etc. And what happens with U(1): do we forcefully get the nonchiral U(1) of electromagnetism, or does it depend of the breaking?

Well, you don't necessarily have to get U(1) EM, because that is a very specific linear combination that survives.

As you say, it is easy and one could expect to find it in some web of solved QFT exercises.

My long shot is to relate the breakings with the compactifications of extra Kaluza Klein dimensions. I would expect Standard Model ---> SU(2) to correspond with a compactification from dimension 10 or 11 to dimension 6.

Well, it depends on what you're compactifying on. You can't break gauge symmetries if you compactify on a circle---you have to compactify on an orbifold. Then you have to figure out where the gauge bosons live, and how to assign them boundary conditions.

 

[BenTheMan]

We'll just have to work it out, I doubt that you'd find it online anywhere. It seems like a non-standard textbook exercize.

 

[Barmecides]

Hello,

don't you have similar example from dynamical breaking of chiral QCD ?

 

[arivero]

Hello,

don't you have similar example from dynamical breaking of chiral QCD ?

Hmm, but there is not Higgs field involved there, is there? In any case I will check Donoghue et al.