A Landau–Ginzburg mirror theorem without concavity

A mirror theorem for toric complete intersections

We prove a generalized mirror conjecture for non-negative complete intersections in symplectic toric manifolds. Namely, we express solutions of the PDE system describing quantum cohomology of such a manifold in terms of suitable hypergeometric functions. 0. Introduction. Let X denote a non-singular compact Kähler toric variety with the Picard number k. The variety X can be obtained by the sympl...

Mirror symmetry without corrections

We give geometric explanations and proofs of various mirror symmetry conjectures for T-invariant Calabi-Yau manifolds when instanton corrections are absent. This uses fiberwise Fourier transformation together with base Legendre transformation. We discuss mirror transformations of (i) moduli spaces of complex structures and complexified symplectic structures, Hp,q’s, Yukawa couplings; (ii) sl (2...

Supergravity Without Light Mirror

We present a spontaneously broken N=2 supergravity model that reduces, in the flat limit MP lanck → ∞, to a globally supersymmetric N=2 system with explicit soft supersymmetry breaking terms. These soft terms generate a mass O(MW ) for mirror quarks and leptons, while leaving the physical fermions light, thereby overcoming one of the major obstacles towards the construction of a realistic N=2 m...

Mirror Symmetry without Corrections

A variety theorem without complementation

The most important tool for classifying recognizable languages is Eilenberg’s variety theorem [1], which gives a one-to-one correspondence between (pseudo)-varieties of finite semigroups and varieties of recognizable languages. Varieties of recognizable languages are classes of recognizable languages closed under union, intersection, complement, left and right quotients and inverse morphisms. R...