We present a practical, algebraic method for efficiently calculating the Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau three-folds with non-standard embeddings. Our methodology covers all of, though is not restricted to, the recently classified positive monads over favourable complete intersection Calabi-Yau three-folds. Since the algorithm is based on manipulating polynomials it can be easily implemented on a computer. This makes the automated investigation of Yukawa couplings for large classes of smooth heterotic compactifications a viable possibility.
We study supersymmetry conditions for the heterotic pure superstring preserving and N=1 supersymmetry in four dimensions directly from the curved superspace defined by the Berkovits-Howe constraints.
We investigate special compactifications of the heterotic string for which the space of half-BPS states is, in a natural way, a representation of various subgroups of the Conway group. These compactifications provide a useful framework for analyzing the action of some of the large symmetry groups appearing in discussions of Moonshine in the physics literature. We investigate toroidal compactifications of heterotic string with sixteen supersymmetries as well as asymmetric toroidal orbifolds with $N=2$ supersymmetry in four dimensions that arise as $K3 \times T^2$ compactifications. The latter C…
We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these techniques relate to algebraic methods for computing holomorphic Yukawa couplings. We apply our methods to various examples and evaluate the holomorphic Yukawa couplings explicitly as functions of the complex structure moduli. It is shown that the rank of the Yukawa matrix can decrease at specific loci in complex structure moduli space. In particular, we co…
We analyze Yukawa unification in the the context of $E_8\times E_8$ heterotic Calabi-Yau models which rely on breaking to a GUT theory via a non-flat gauge bundle and subsequent Wilson line breaking to the standard model. Our focus is on underlying GUT theories with gauge group $SU(5)$ or $SO(10)$. We provide a detailed analysis of the fact that, in contrast to traditional field theory GUTs, the underlying GUT symmetry of these models does not enforce Yukawa unification. Using this formalism, we present various scenarios where Yukawa unification can occur as a consequence of additional symmetr…
We compute the one-loop threshold corrections to the gauge and gravitational couplings for a large class of N=2 non-Kähler heterotic compactifications with three-form flux, consisting in principal two-torus bundles over K3 surfaces. We obtain the results as sums of BPS-states contributions, depending on the topological data of the bundle. We analyse also the worldsheet non-perturbative corrections coming from instantons wrapping the torus fiber, that are mapped under S-duality to D-instanton corrections in type I flux compactifications.
We study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest non-trivial elliptic fibration the effect is quite dramatic: the $I_1$ degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the $T^2$. This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from t…
We present a new class of dualities relating non-geometric Calabi-Yau compactifications of type II string theory to T-fold compactifications of the heterotic string, both preserving four-dimensional $\mathcal{N}=2$ supersymmetry. The non-geometric Calabi-Yau space is a $K3$ fibration over $T^2$ with non-geometric monodromies in the duality group $O(Γ_{4,20})$; this is dual to a heterotic reduction on a $T^4$ fibration over $T^2$ with the $O(Γ_{4,20})$ monodromies now viewed as heterotic T-dualities. At a point in moduli space which is a minimum of the scalar potential, the type II compactifica…
We study the constraints of spacetime supersymmetry for perturbative three- and two-dimensional Minkowski vacua of the critical heterotic string. Assuming a standard RNS construction of the spacetime supersymmetry generators and a compact unitary internal superconformal worldsheet theory, we describe the worldsheet structures associated to various spacetime supersymmetries. In three dimensions we show that there are no CFT surprises: each allowed spacetime supersymmetry is realized by a supergravity compactification. As a recent orbifold construction shows, in two dimensions there are more exo…
A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail compactifications on a circle, where we find all the maximal gauge symmetry groups and the points where they arise. We show the gauge symmetry groups that arise at special points, in figures of slices of the 17-dimensional moduli space of Wilson lines and circle radii. We then study the target space realization of the duality symmetry. Although the global continuo…
The Mordell-Weil lattices (MW lattices) associated to rational elliptic surfaces are classified into 74 types. Among them, there are cases in which the MW lattice is none of the weight lattices of simple Lie algebras or direct sums thereof. We study how such "non-Cartan MW lattices" are realized in the six-dimensional heterotic/F-theory compactifications. In this paper, we focus on non-Cartan MW lattices that are torsion free and whose associated singularity lattices are sublattices of $A_7$. For the heterotic string compactification, a non-Cartan MW lattice yields an instanton gauge group $H$…
