From what I understand the Standard Model (gauge) symmetry group U(1)xSU(2)LxSU(3) was originally pieced together from experimental observations.

What theories do we have to try and explain the origin of this symmetry group? If there are no such theories, how then should we go about trying to find a theory to explain the Standard Model?

Two possibilities I can think of are:

1. Matter might be topological in nature and so perhaps the Standard Model symmetries emerge from the underlying topology of particles;

2. The symmetries of the Standard Model somehow drop out from space-time symmetries.

With regards to the second possibility, It seems that 'no-go' theorems (Coleman Mandula theorem) say that space-time and internal symmetries can only be combined in a trivial way (direct product). Are there (sensible) ways around these theorems?

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