| Summary: | In this letter, we follow the hypothesis that the tangent bundle (TB) with the central extended little groups
of the SO(3, 1)⋊T(1, 3) group as gauge group is the underlying geometric structure for a unified theory of
the fundamental physical interactions. Based on the geometry of the TB, recently, I presented a generalized
theory of electroweak interaction in [1]. The vertical (internal) Laplacian of the tangent bundle possesses
the same form as the Hamiltonian of a 2D semiconductor quantum Hall system. The three families of
leptons and quarks, unlike in the SM, are distinguished by a new quantum number. Here, it will be shown
that the SU(3) color symmetry for strong interaction arises as an emergent symmetry similar to Chern-
Simon gauge symmetries in multicomponent quantum Hall systems and fractional charge quantization of
quarks can be understood by a binding of two vortices to a quark, turning it into a composite quark. The
analogy with the anomalous quantum Hall effect could hint at the possible existence of exotic quark states
with a hypercharge of e/5. Note that based on translational transformations in the TB geometry previously
a gauge theoretical understanding of gravity has been achieved. Therefore, the TB can be considered as the
underlying geometry that could constitute a possible way for the unification of the known fundamental
forces.
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