2009/04/30 by Ignatios Antoniadis, I. Antoniadis, Alok Kumar +1 · 55 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane cosmology #Fermion #Mathematical physics #Mathematics #Orientifold #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scalar (mathematics) #Theoretical physics #Wave function #Yukawa potential #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.nuclphysb.2009.08.002
published in Nuclear Physics B 823(1-2), 116-173 (Elsevier BV) · 77 pages, v2:Some additions and improvements in text, version to appear in Nucl. Phys. B
arxiv created 2009/08/10 · openalex publication_date 2009/08/11 · arxiv updated 2010/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 arXiv:0709.2799.