Abstract
We calculate non-perturbative contributions to Yukawa couplings on D3-branes at orbifold singularities due to E3 and fractional E(-1) instantons which do not intersect the visible sector branes. While distant E3 instantons on bulk cycles typically contribute to Yukawa couplings, we find that distant fractional E(-1) can also give rise to new Yukawa couplings. However, fractional E(-1) instantons only induce Yukawa couplings if they are located at a singularity which shares a collapsed homologous two-cycle with the singularity supporting the visible sector. The non-perturbative contributions to Yukawa couplings exhibit a different flavour structure than the tree-level Yukawa couplings and, as a result, they can be sources of flavour violation. This is particularly relevant for schemes of moduli stabilisation which rely on superpotential contributions from E3 instantons, such as KKLT or the Large Volume Scenario. As a byproduct of our analysis, we shed some new light on the properties of annulus diagrams with matter field insertions in stringy instanton calculus.
Highlights
This last point is of interest to phenomenologists for various reasons
While distant E3 instantons on bulk cycles typically contribute to Yukawa couplings, we find that distant fractional E(-1) can give rise to new Yukawa couplings
The vertex operator for this field Vθ−1/2 having worldsheet coordinate z is e−φ/2jα(z), where jα is the current of the supersymmetry preserved by the D-branes of the theory but broken by the instanton, and
Summary
We are interested in extracting holomorphic couplings in the effective supergravity theory; these benefit from the powerful supersymmetric non-renormalisation theorems. The form for the tree-level superpotential is recognised as arising from worldsheet instantons It can be further restricted when we consider the exact gauging of the axionic symmetries, and how the matter fields transform under them. For the gauge kinetic function fa (of a given D6 brane) we know that the tree-level piece, being proportional to the string coupling, must be a linear combination of the complex structure moduli (a linear shift in the gauge kinetic function being permitted as a shift in the theta angle); while the one-loop correction must be independent of the UI since it must be independent of the string coupling. Complex structure moduli in type IIB do not have axionic shifts; instead the H−2,1 and H−1,2 forms make up h2−,1 complex scalars zI , independent of the string coupling.
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