Importance in Physics
N = 8 supergravity in four dimensions, which is a dimensional reduction from 11 dimensional supergravity, admit an E7 bosonic global symmetry and an SU(8) bosonic local symmetry. The fermions are in representations of SU(8), the gauge fields are in a representation of E7, and the scalars are in a representation of both (Gravitons are singlets with respect to both). Physical states are in representations of the coset E7 / SU(8).
In string theory, E7 appears as a part of the gauge group of one the (unstable and non-supersymmetric) versions of the heterotic string. It can also appear in the unbroken gauge group E8 × E7 in six-dimensional compactifications of heterotic string theory, for instance on the four-dimensional surface K3.
Read more about this topic: E7 (mathematics)
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