Importance in Physics
N=8 supergravity in five dimensions, which is a dimensional reduction from 11 dimensional supergravity, admits an E6 bosonic global symmetry and an Sp(8) bosonic local symmetry. The fermions are in representations of Sp(8), the gauge fields are in a representation of E6, and the scalars are in a representation of both (Gravitons are singlets with respect to both). Physical states are in representations of the coset E6/Sp(8).
In grand unification theories, E6 appears as a possible gauge group which, after its breaking, gives rise to the SU(3) × SU(2) × U(1) gauge group of the standard model (also see Importance in physics of E8). One way of achieving this is through breaking to SO(10) × U(1). The adjoint 78 representation breaks, as explained above, into an adjoint 45, spinor 16 and as well as a singlet of the SO(10) subalgebra. Including the U(1) charge we have
Where the subscript denotes the U(1) charge.
Read more about this topic: E6 (mathematics)
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