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Type IIA on a compact Calabi-Yau and \(D = 11\) supergravity uplift of its orientifold. (English) Zbl 1062.83088

The author considers \(N=2\) type II theory compactified on the Calabi-Yau 3-fold, which is defined as the degree-24 Fermat hypersurface \[ z_1^{24}+ z_2^{24}+ z_3^{12}+ z_4^3 + z_5^2 =0 \] in the weighted projective space W\(\mathbb{C}\text{P}^4 (1,1,2,8,12)\). He resolves singularities and following Hori and Wafa derives the Picard-Fuchs equation for the periodic integrals in the corresponding Landau-Ginsburg theory. The problem of description of solutions of this equation is discussed. The Kähler potential in the large volume limit of the Calabi-Yau manifold is evaluated. A conjecture about the action of the antiholomorphic involution on the periods of the Calabi-Yau manifold is given. It is verified for the torus \(T^6\) and partially for the mirror dual of the quintic.

MSC:

83E50 Supergravity
83E30 String and superstring theories in gravitational theory
14J81 Relationships between surfaces, higher-dimensional varieties, and physics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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