spin geometry, string geometry, fivebrane geometry …
rotation groups in low dimensions:
see also
The Scherk-Schwarz mechanism (Scherk-Schwarz 79) is the spontaneous supersymmetry breaking by KK-compactification on a circle whose spin structure imposes anti-periodic boundary conditions for fermion fields.
In the Witten-Sakai-Sugimoto model non-supersymmetric QCD is geometrically engineered from the D=5 super Yang-Mills theory on D4-branes by wrapping these on a Scherk-Schwarz circle (Witten 98, p. 19)
The original articles:
Joël Scherk, John Schwarz, Spontaneous breaking of supersymmetry through dimensional reduction, Physics Letters B Volume 82, Issue 1, 12 March 1979, Pages 60-64 (doi:10.1016/0370-2693(79)90425-8)
Joël Scherk, John Schwarz, How to get masses from extra dimensions, in: Supergravities in Diverse Dimensions, pp. 1282-1309 (1989) (doi:10.1142/9789814542340_0083)
In geometrically engineering of non-supersymmetric QCD from the D=5 super Yang-Mills theory on D4-branes by wrapping these on a Scherk-Schwarz circle (the Witten-Sakai-Sugimoto model):
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