For maximal supergravity on Riemann-flat Bieberbach manifolds, the Kaluza-Klein spectrum can be reorganized so that all supertraces vanish up to mass power eight, yielding a finite, negative one-loop potential.
Spin structures on flat manifolds
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We present an algorithmic approach to the problem of existence of spin structures on flat manifolds. We apply our method in the cases of flat manifolds of dimensions 5 and 6.
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Supersymmetry-breaking compactifications on Riemann-flat manifolds
For maximal supergravity on Riemann-flat Bieberbach manifolds, the Kaluza-Klein spectrum can be reorganized so that all supertraces vanish up to mass power eight, yielding a finite, negative one-loop potential.