منابع مشابه
On Calabi-Yau supermanifolds
We prove that a Kähler supermetric on a supermanifold with one complex fermionic dimension admits a super Ricci-flat supermetric if and only if the bosonic metric has vanishing scalar curvature. As a corollary, it follows that Yau’s theorem does not hold for supermanifolds. Calabi[1] proposed that if a Kähler manifold has vanishing first Chern class, that is, the Ricci-form obeys Rij̄(g) = ∂iv̄j ...
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We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying...
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We study the Ricci flatness condition on generic supermanifolds. It has been found recently that when the fermionic complex dimension of the supermanifold is one the vanishing of the super-Ricci curvature implies the bosonic submanifold has vanishing scalar curvature. We prove that this phenomena is only restricted to fermionic complex dimension one. Further we conjecture that for complex fermi...
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We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super Landau-Ginzburg theories. In some cases the dual can be equivalent to a geometry. We apply this to some examples. In particular we show that the mirror of the twistorial Calabi-Yau CP becomes equivalent to a quadric in CP×CP as had been recently conjectured (in the limit where the Kähler parameter of CP, t → ±∞...
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As been recently pointed out, physically relevant models derived from string theory require the presence of non-vanishing form fluxes besides the usual geometrical constraints. In the case of NS-NS fluxes, the Generalized Complex Geometry encodes these informations in a beautiful geometrical structure. On the other hand, the R-R fluxes call for supergeometry as the underlying mathematical frame...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1980
ISSN: 0002-9947
DOI: 10.2307/1998294