# Is the search for a Simple-group-based Electro-Weak theory over?

Just wondering:

We know that, in its current form of the $SU(2)_L\times U(1)$, the electroweak theroy rides a wave of huge success. However, is it not possible that the correct simple group unification could reveal physics that the current model doesn’t?

For example, it could reveal the existence of a unique gauge boson, like the photon for EM ('EM-photon') produced by $U(1)$ invariance, which might be called the 'EW-photon.’ This EW-photon, with the right group structure, could then produce the $W^+,W^-,Z_0$ and the EM-photon and the known physics at the E-W scale?

Does anybody know whether there is any activity on this, other than Technicolour? Links will be greately appreciated.

• Would you count Grand Unified Theories? They incorporate the electroweak theory and are usually based on simple gauge groups. – user1504 Mar 1 '13 at 0:41
• Just to extend user1504's comment, popular groups are SU(5), SO(10), and nowadays you hear about exotica like E8. In all cases the full standard model SU(3)xSU(2)xU(1) is embedded. – Michael Brown Mar 1 '13 at 10:15
• Sorry, Michael, you meant $E_6$, not $E_8$, right? There can't be any GUT (QFT) based on $E_8$ because that group only has real representations but we need complex ones for chiral fermions and $E_6$ is the only exceptional compact Lie group that has complex reps. In string theory, all these things may be embedded into an $E_8$ but the breaking of $E_8$ to a lower group requires stringy phenomena - it can't proceed by field-theory mechanisms such as the Higgs mechanism. All papers/media hype talking about $E_8$ unifying field theories are dumb pseudoscience. – Luboš Motl Mar 1 '13 at 13:11
• @Michael Brown Thank you for the suggestions. I like the mathematical structure of the groups you are suggesting, or the $E_6$ of Lubos Motl. Although these are mathematically consistent structures in the way they embed the lower symmetries and break into these groups, this is where the problem lies from physics point of view. My interest is at the electroweak level. These groups, by breaking in the above way, do not bring in any new physics. I think something more fundamental than mathematical consistency is missing from these models. Any other suggestions please? – JKL Mar 1 '13 at 23:34