Wave functions and Yukawa couplings in local string compactifications

Abstract

We consider local models of magnetised D7 branes in IIB string compactifications, focussing on cases where an explicit metric can be written for the local 4-cycle. The presence of an explicit metric allows analytic expressions for the gauge bundle and for the chiral matter wavefunctions through solving the Dirac and Laplace equations. The triple overlap of the normalised matter wavefunctions generates the physical Yukawa couplings. Our main examples are the cases of D7 branes on P 1 × P 1 and P 2 . We consider both supersymmetric and non-supersymmetric gauge backgrounds and both Abelian and non-Abelian gauge bundles. We briefly outline potential phenomenological applications of our results.

Three generation magnetized orbifold models

“…Here we show the model with (|I (1) ab |, |I (1) ca |, |I (1) bc |) = (7,8,15). The following table shows zeromode wavefunctions of left, right-handed matter fields and Higgs fields.…”

Wavefunctions on magnetized branes in the conifold

“…On the other hand, there are some studies for the local magnetized D7-brane models on the curved backgrounds such as P 1 , P 1 × P 1 and P 2 [6] and the authors of ref. [6] show the explicit matter wavefunctions.…”

“…[6] show the explicit matter wavefunctions. So far, the local models are considered to be embedded in some global CY threefold.…”

“…where Γ κ is the kappa-symmetry matrix, 6) in the case of D7-brane, ǫ denotes Killing spinor for Klebanov-Witten background (2.4) and γ µ 1 ···µ 8 is the antisymmetrized product of the gamma matrices pull-backed into the…”

"Big" Divisor D3/D7 Swiss-Cheese Phenomenology

“…and their fermionic superpartners χ I that are valued, e.g., in the adj(U (3 QCD + 2 EW )) to begin with, decompose into the bifundamentals (3 QCD ,2 EW ) and its complex conjugate, corresponding to the bifundamental left-handed quarks of the Standard Model (See [19]). …”