Merging heterotic orbifolds and K3 compactifications with line bundles

Abstract

Abstract:We clarify the relation between six-dimensional Abelian orbifold compactifications of the heterotic string and smooth heterotic K3 compactifications with line bundles for both SO(32) and E 8 × E 8 gauge groups. The T 4 /Z N cases for N = 2, 3, 4 are treated exhaustively, and for N = 6 some examples are given. While all T 4 /Z 2 and nearly all T 4 /Z 3 models have a simple smooth match involving one line bundle only, this is only true for some T 4 /Z 4 and T 4 /Z 6 cases. We comment on possible matchings with more than one line bundle for the remaining cases. The matching is provided by comparisons of the massless spectra and their anomalies as well as a field theoretic analysis of the blow-ups.

F-theory on all toric hypersurface fibrations and its Higgs branches

“…This is guaranteed by imposing flatness of the D-term potential along the direction of the VEV. As it has been observed in [92], for the case of a Higgs field that is not in the adjoint representation, at least two hyper multiplets with identical quantum numbers have to acquire a VEV in order to achieve a D-flat direction. Furthermore, the Higgs mechanism of interest here has to relate two toric hypersurface fibrations.…”

N $$ \mathcal{N} $$ =2 heterotic string compactifications on orbifolds of K3 × T 2

“…The hypers for the g orbifold are 2(56, 1) + 16(1, 1). 3 Twisted by g 2 . It in only in this sector we really need to explicitly work out the details of the states and using the formula (3.26).…”

Non-abelian bundles on heterotic non-compact K3 orbifold blowups

“…In recent publications we have made first attempts to understand the relation between heterotic string orbifold constructions and smooth Calabi-Yau manifolds with gauge bundles (see [24] for earlier work). To this end we have constructed explicit blowups of C n /Z n orbifolds with Abelian gauge backgrounds satisfying the Hermitean Yang-Mills equations.…”

“…This field strength is obtained from the gauge connection given by 24) where ω r is defined from V r via the equation (2.8). The normalization of the gauge connections A r above has been chosen such that the corresponding gauge field strengths F r define an orthonormal basis of self-dual two forms [40,41] 25) where the integral is performed over the whole Eguchi-Hanson space.…”

“…The spectra for the pure line bundle models agree with those given in ref. [24]; the other spectra are novel except that of the standard embedding.…”