Prof Andre Lukas

Abstract:

We propose an analytic method to calculate the matter field Kähler metric in heterotic compactifications on smooth Calabi-Yau three-folds with Abelian internal gauge fields. The matter field Kähler metric determines the normalisations of the N = 1 chiral superfields, which enter the computation of the physical Yukawa couplings. We first derive the general formula for this Kähler metric by a dimensional reduction of the relevant supergravity theory and find that its T-moduli dependence can be determined in general. It turns out that, due to large internal gauge flux, the remaining integrals localise around certain points on the compactification manifold and can, hence, be calculated approximately without precise knowledge of the Ricci-flat Calabi-Yau metric. In a final step, we show how this local result can be expressed in terms of the global moduli of the Calabi-Yau manifold. The method is illustrated for the family of Calabi-Yau hypersurfaces embedded in P1 × P3 and we obtain an explicit result for the matter field Kähler metric in this case.

Abstract:

We analyze heterotic line bundle models on elliptically fibered Calabi-Yau three-folds over weak Fano bases. In order to facilitate Wilson line breaking to the standard model group, we focus on elliptically fibered three-folds with a second section and a freely-acting involution. Specifically, we consider toric weak Fano surfaces as base manifolds and identify six such manifolds with the required properties. The requisite mathematical tools for the construction of line bundle models on these spaces, including the calculation of line bundle cohomology, are developed. A computer scan leads to more than 400 line bundle models with the right number of families and an SU(5) GUT group which could descend to standard-like models after taking the ℤ2 quotient. A common and surprising feature of these models is the presence of a large number of vector-like states.