Abstract
We construct a chiral theory of gravity in seven and eight dimensions, which is equivalent to Einstein–Cartan theory using fewer variables. In these dimensions, we can construct such higher-dimensional chiral gravity because of the existence of the gravitational instanton. The octonionic-valued variables in the theory represent the deviation from the gravitational instanton, and from their non-associativity, prevent the theory being SO(n) gauge invariant. Still the chiral gravity holds G2 (7D), and spin(7) (8D) gauge symmetry.
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