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## Main Question or Discussion Point

Hello everyone!

Im new on this forum, have been lurking around paying attention to all the interesting stuff you guys talk about, and now iv joined up!!

Firstly, I am not sure if im posting in the right place - there isnt really a distinct place for a question like this. Hopefully im in the right place.

So basically, here is the question, recently i have been working through kaluza klein theory, more specifically the original one. i.e. S^1 compactified under the usual U(1) gauge, we gain a gauge field in which we quantise around the circle, we truncate our final action and gain a low-energy action whereby coupled EM and GR field equations come out. I do know there are issues with this truncation as, we cant really truncate massive to massless fields without actually losing massless fields.

However, im trying to figure out what would happen in a sphere. What im basically starting off with is some generalised arbitrary Yang-Mills theory, SU(2), and trying to unify this with gravity. However, some opinions have arisen. Essentially what i would like to do is gain coupled equations for the weak nuclear field and einstein field equations. So im sort of trying to equate SO(3) and SU(2) (I know that is said without rigor). I have a set of killing vectors for SO(3), of which i assume make make the lie algebra, also i have the yang mills theory, i.e. a generalised non-abelian theory, i have lie algebra and the field strength for this too.

The problem is that, i have been told that it might not work, as the Ricci flatness equation will not come out. This being due to S^2 having positive curvature, whilst in the original theory we only had a S^1 which in flat... iv been told the theory works better with a torus ie. U(1)^n. The issue i have with this is that i wouldve hope to try an unite weak force and gravity, and under U(1)^n i would just be getting EM in some higher dimension.

any help would be greatly appreciated, hopefully one of you guys can tell me whats up.

cheers

Im new on this forum, have been lurking around paying attention to all the interesting stuff you guys talk about, and now iv joined up!!

Firstly, I am not sure if im posting in the right place - there isnt really a distinct place for a question like this. Hopefully im in the right place.

So basically, here is the question, recently i have been working through kaluza klein theory, more specifically the original one. i.e. S^1 compactified under the usual U(1) gauge, we gain a gauge field in which we quantise around the circle, we truncate our final action and gain a low-energy action whereby coupled EM and GR field equations come out. I do know there are issues with this truncation as, we cant really truncate massive to massless fields without actually losing massless fields.

However, im trying to figure out what would happen in a sphere. What im basically starting off with is some generalised arbitrary Yang-Mills theory, SU(2), and trying to unify this with gravity. However, some opinions have arisen. Essentially what i would like to do is gain coupled equations for the weak nuclear field and einstein field equations. So im sort of trying to equate SO(3) and SU(2) (I know that is said without rigor). I have a set of killing vectors for SO(3), of which i assume make make the lie algebra, also i have the yang mills theory, i.e. a generalised non-abelian theory, i have lie algebra and the field strength for this too.

The problem is that, i have been told that it might not work, as the Ricci flatness equation will not come out. This being due to S^2 having positive curvature, whilst in the original theory we only had a S^1 which in flat... iv been told the theory works better with a torus ie. U(1)^n. The issue i have with this is that i wouldve hope to try an unite weak force and gravity, and under U(1)^n i would just be getting EM in some higher dimension.

any help would be greatly appreciated, hopefully one of you guys can tell me whats up.

cheers