Related papers: Lattices: From Roots to String Compactifications
In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-Theory compactified on an elliptic K3 surface for the case of an unbroken E8 x E8 gauge group. The explicit map relating the deformation…
We study fibrations by elliptic curves and K3 surfaces of double octic Calabi-Yau threefolds determined by singular lines and points of multiplicity at least 4 of the defining octic arrangement. As a consequence we conclude that every…
Reflexive polygons have been extensively studied in a variety of contexts in mathematics and physics. We generalize this programme by looking at the 45 different lattice polygons with two interior points up to SL(2,$\mathbb{Z}$)…
In this work we systematically enumerate genus one fibrations in the class of 7,890 Calabi-Yau manifolds defined as complete intersections in products of projective spaces, the so-called CICY threefolds. This survey is independent of the…
We classify complex K3 surfaces of zero entropy admitting an elliptic fibration with only irreducible fibers. These surfaces are characterized by the fact that they admit a unique elliptic fibration with infinite automorphism group. We…
During the last years we have generated a large number of data related to Calabi-Yau hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified all reflexive polyhedra in three dimensions leading to K3…
We present several new examples of nontrivial 4d N=1 superconformal field theories. Some of these theories exhibit exotic global symmetries, including non-simply laced groups (such as $F_4$). They are obtained by studying threebrane probes…
We study heterotic asymmetric orbifold models. By utilizing the lattice engineering technique, we classify (22,6)-dimensional Narain lattices with right-moving non-Abelian group factors which can be starting points for Z3 asymmetric…
Discrete gauge groups naturally arise in F-theory compactifications on genus-one fibered Calabi-Yau manifolds. Such geometries appear in families that are parameterized by the Tate-Shafarevich group of the genus-one fibration. While the…
We study fundamental groups of toroidal compactifications of non compact ball quotients and show that the Shafarevich conjecture on holomorphic convexity for these complex projective manifolds is satisfied in dimension 2 provided the…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in terms of lattice theory. As a result, we prove the…
We study the elliptic genera of the non-critical strings of six dimensional superconformal field theories from the point of view of the strings' worldsheet theory. We formulate a general ansatz for these in terms of characters of the affine…
We construct compact examples of D-manifolds for type IIB strings. The construction has a natural interpretation in terms of compactification of a 12 dimensional `F-theory'. We provide evidence for a more natural reformulation of type IIB…
We construct several examples of genus-one fibered K3 surfaces without a global section with type $I_{n}$ fibers, by considering double covers of a special class of rational elliptic surfaces lacking a global section, known as Halphen…
A systematic analysis is presented of compactifications of the IIB superstring on $AdS_5 \times S^5/\Gamma$ where $\Gamma$ is a non-abelian discrete group. Every possible $\Gamma$ with order $g \leq 31$ is considered. There exist 45 such…
We use the latest techniques in machine-learning to study whether from the landscape of Calabi-Yau manifolds one can distinguish elliptically fibred ones. Using the dataset of complete intersections in products of projective spaces (CICY3…
We study four dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K\"{a}hler structure. Using intersecting complex toric surfaces, we derive a class of N=1 quivers with charged fundamental matter placed on…
We investigate gauge theories and matter contents in F-theory compactifications on families of genus-one fibered Calabi-Yau 4-folds lacking a global section. To construct families of genus-one fibered Calabi-Yau 4-folds that lack a global…
Multiflavor gauge theories of matter systems on a three-dimensional lattice have recently been widely investigated especially in connection with a possible symmetry enlargement at a continuous phase transition. Abelian models were studied…