Computing Yukawa Couplings from Magnetized Extra Dimensions

Abstract

We compute Yukawa couplings involving chiral matter fields in toroidal compactifications of higher dimensional super-Yang-Mills theory with magnetic fluxes. Specifically we focus on toroidal compactifications of D=10 super-Yang-Mills theory, which may be obtained as the low-energy limit of Type I, Type II or Heterotic strings. Chirality is obtained by turning on constant magnetic fluxes in each of the 2-tori. Our results are general and may as well be applied to lower D = 6, 8 dimensional field theories. We solve Dirac and Laplace equations to find out the explicit form of wavefunctions in extra dimensions. The Yukawa couplings are computed as overlap integrals of two Weyl fermions and one complex scalar over the compact dimensions. In the case of Type IIB (or Type I) string theories, the models are T-dual to (orientifolded) Type IIA with D6-branes intersecting at angles. These theories may have phenomenological relevance since particular models with SM group and three quark-lepton generations have been recently constructed. We find that the Yukawa couplings so obtained are described by Riemann ϑ-functions, which depend on the complex structure and Wilson line backgrounds. Different patterns of Yukawa textures are possible depending on the values of these backgrounds. We discuss the matching of these results with the analogous computation in models with intersecting D6-branes. Whereas in the latter case a string computation is required, in our case only field theory is needed. JHEP 8. A 3-generation MSSM-like Model 56 9. Final comments and conclusions 59 A. Dimensional Reduction of N=1 Super Yang-Mills 61 B. Fluxes and supersymmetry 64 B.1 Hermitian Yang-Mills Equations 64 B.2 D-brane interpretation 66 B.3 Mirror symmetry and string corrections 67JHEP (i, j, k) dependence of the Yukawa coupling. In a SUSY compactification the (holomorphic) superpotential should be identified with this product of ϑ-functions, whereas the rest of the factors should come from D-term normalization of three-point functions.As we said, the natural setting for studying compactifications of D=10 super Yang-Mills is string theory, since it appears naturally in the effective field theory limit of Type I, Type IIB (with D9-branes) and heterotic strings. In fact, although the mentioned compactification and computations may be performed without any reference to string theory, in the present paper we will have always in mind the string theory point of view. In particular it is well known that Type IIB theory with D9-branes compactified on a (magnetized) T 6 is T-dual to Type IIA theory with D6-branes wrapping 3-cycles on T 6 and intersecting at angles. 3 In recent years string models with intersecting D-branes have been actively pursued in order to obtain realistic models of particle physics [4,6,[18][19][20]. The main motivation for this is that in these schemes chiral fermions naturally appear at the points in compact space in which Dp-branes intersect. Furthermore, since Dp-branes may intersect multiple times, this gives a rationale for the...

Z N twisted orbifold models with magnetic flux

“…Torus compactifications with some magnetic fluxes are quite interesting extradimensional backgrounds [1][2][3][4][5]. 1 That can realize chiral spectra in four-dimensional low energy effective field theory.…”

Supersymmetric radiative flavour

“…first two graphs have on their left hand side a structure that is precisely the same as that found in the 2-loop case. When s = 0, the explicit evaluation of the 2-loop graphs leading to (2.20) in fact shows that the loop integral gives a finite value that is independent of p. The first two graphs of figure 4 therefore give the same as the first graph of figure 2, multiplied by an overall factor of 3ζ(3) (λλ * ) 2 (4π) 4 . This will combine with the analogue of the second graph of figure 2.…”

“…Assuming that the scalar 4-point function does receive the 2-loop correction required by supersymmetry, this is provided by the third graph of figure 4. The 4-loop graph then entirely factorises into two 2-loop integrals, giving an overall magnitude of 3ζ(3) (λλ * ) 2 (4π) 4 …”

“…This restricted rank structure has appeared for heterotic models [1,2], IIA and IIB intersecting brane models [3,4], IIB models of branes at singularities [5,6] and F-theory models [7,8]. It is important to understand the physics that can generate rank three Yukawa couplings.…”

Neutrino masses, Baryon asymmetry, dark matter and the moduli problem — A complete framework

“…This is still consistent with the supergravity approximation. The un-normalized yukawa couplings h D arise from multiply wrapped world-sheet instantons and are given by products of Jacobi theta functions [45]. These can be well approximated as h ijk D ≈ O(1)e −η ijk 4πUm where η ijk = O(1).…”