Anomalies and fermion content of grand unified theories in extra dimensions

The restrictions imposed by anomaly cancellation on the chiral fermion content of nonsupersymmetric gauge theories based on various groups are studied in spacetime dimension D=6, 8, and 10. In particular, we show that the only mathematically consistent chiral SU(5) theory in D=6 contains three nonidentical generations.

11.10.Kk
12.10.Dm
gauge field theory: SU(3) x SU(2) x U(1)
gauge field theory: SU(5)
gauge field theory: SO(10)
gauge field theory: E(8)
dimension: 6
dimension: 8
dimension: 10
supersymmetry

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