Premium
The effective action of type II Calabi‐Yau orientifolds
Author(s) -
Grimm T.W.
Publication year - 2005
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200510253
Subject(s) - superpotential , orientifold , calabi–yau manifold , type (biology) , physics , mirror symmetry , moduli , instanton , multiplet , theoretical physics , f theory , mathematical physics , supersymmetry , string theory , pure mathematics , quantum mechanics , mathematics , ecology , biology , spectral line
This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB Calabi‐Yau orientifolds in the presence of background fluxes by using a Kaluza‐Klein reduction. The Kähler potential, the gauge kinetic functions and the flux‐induced superpotential are determined in terms of geometrical data of the Calabi‐Yau orientifold and the background fluxes. As a new result, it is shown that the chiral description directly relates to Hitchin's generalized geometry encoded by special odd and even forms on a threefold, whereas a dual formulation with several linear multiplets makes contact to the underlying N = 2 special geometry. In type IIB setups, the flux‐potentials can be expressed in terms of superpotentials, D‐terms and, generically, a massive linear multiplet. The type IIA superpotential depends on all geometric moduli of the theory. It is reviewed, how type IIA orientifolds arise as a special limit of M‐theory compactified on specific G 2 manifolds by matching the effective actions. In a similar spirit type IIB orientifolds are shown to descend from F‐theory on a specific class of Calabi‐Yau fourfolds. In addition, mirror symmetry for Calabi‐Yau orientifolds is briefly discussed and it is shown that the N = 1 chiral coordinates linearize the appropriate instanton actions.