Why Start Theories with SO(n,1) and Compactify to SO(3,1)xG?

[timb00]

Hi how,

in my master project I am working on extra dimensions and I am asking my self
why is it common to start most of the theories with a space time symmetry given by
SO(n,1) (n>4) and then compactify the obtained spectrum to SO(3,1)xG (where G is an abitrary symmetry group).

Because I think there might be other groups which have the SO(3,1) as subgroup as well?

In my question I said that "most of the theories" working in such a way. This means that all models I have seen, working in that fashion.

I hope you understand my question, otherwise ask and i will do my best to explain my
question further.

best regards,

timb00

P.s. : sorry for my bad English.

 

[haushofer]

Because then you start out with having Lorentz symmetry in the whole space. What kind of spacetime symmetries in the whole space would you propose? :)

 

[Jakeman002]

Because there is a finite amount of groups and the bigger they get the more symmetries they contain. They usually look at SO(p,q) bigger than S0(3,1) in spatial dimensions because the conformal group doesn't have enough symmetry hence moving to a bigger rotation group will allow for more symmetry and then you can compactify the extra spatial dimensions to get around that. Also going back to what I said about a finite amount of groups you can look at dynkin diagrams to show you this hence finding a group that contains S0(3,1) is not unique.