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Fermion wavefunctions in magnetized branes: theta identities and Yukawa couplings. (English) Zbl 1196.81188
Summary: Computation of Yukawa couplings, determining superpotentials as well as the Kähler metric, with oblique (non-commuting) fluxes in magnetized brane constructions is an interesting unresolved issue, in view of the importance of such fluxes for obtaining phenomenologically viable models. In order to perform this task, fermion (scalar) wavefunctions on toroidally compactified spaces are presented for general fluxes, parameterized by Hermitian matrices with eigenvalues of arbitrary signatures. We also give explicit mappings among fermion wavefunctions, of different internal chiralities on the tori, which interchange the role of the flux components with the complex structure of the torus. By evaluating the overlap integral of the wavefunctions, we give the expressions for Yukawa couplings among chiral multiplets arising from an arbitrary set of branes (or their orientifold images). The method is based on constructing certain mathematical identities for general Riemann theta functions with matrix valued modular parameter. We briefly discuss an application of the result, for the mass generation of non-chiral fermions, in the \(SU(5)\) GUT model presented by us in Antoniadis, Kumar and Panda (2008).

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V22 Unified quantum theories
32Q15 Kähler manifolds
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