>>11211220well first of all red+green is not antiblue. the opposite of antiblue is blue which is not equal to red+green in the theory of gluons
in terms of KK theories or supergravity theories, the gauge groups arising from compactified dimensions have little to do with quantum theory. the original KK theories and the ones einstein investigated were purely classical. the considerations of gauge groups that arise from compactified dimensions are mostly classical, and quantizing them usually only amounts to "corrections" to particular phenomena in the classical gauge theory. like for example, as i mentioned, anomalies, as well as renormalization flows.
so basically the best way to think about kaluza-klein theories and higher-dimensional theories like string theory is more like "let's try to get a gauge group we want from this theory and then check the quantum corrections." in fact in string theory it goes more like "let's try to get a gauge group, then check stringy corrections, and after that check quantum corrections"
non-string KK theories like supergravity were all doomed by their quantum corrections. the lesson is that it is not easy to build a consistent KK theory that isn't ruined by quantum effects
