Explore the vast range of titles available.

A bstract Eight-dimensional nongeometric heterotic strings were constructed as duals of F-theory on Λ 1,1 ⊕ E 8 ⊕ E 7 lattice polarized K3 surfaces by Malmendier and Morrison. We study the structure of the moduli space of this construction. There are special points in this space at which the ranks of the non-Abelian gauge groups on the 7-branes in F-theory are enhanced to 18. We demonstrate that the enhanced rank-18 non-Abelian gauge groups arise as a consequence of the coincident 7-branes, which deform stable degenerations on the F-theory side. This observation suggests that the non-geometric heterotic strings include nonperturbative effects of the coincident 7-branes on the F-theory side. The gauge groups that arise at these special points in the moduli space do not allow for perturbative descriptions on the heterotic side. We also construct a family of elliptically fibered Calabi-Yau 3-folds by fibering K3 surfaces with enhanced singularities over ℙ 1 . Highly enhanced gauge groups arise in F-theory compactifications on the resulting Calabi-Yau 3-folds.

A bstract We constructed several families of elliptic K3 surfaces with Mordell-Weil groups of ranks from 1 to 4. We studied F-theory compactifications on these elliptic K3 surfaces times a K3 surface. Gluing pairs of identical rational elliptic surfaces with nonzero Mordell-Weil ranks yields elliptic K3 surfaces, the Mordell-Weil groups of which have nonzero ranks. The sum of the ranks of the singularity type and the Mordell-Weil group of any rational elliptic surface with a global section is 8. By utilizing this property, families of rational elliptic surfaces with various nonzero Mordell-Weil ranks can be obtained by choosing appropriate singularity types. Gluing pairs of these rational elliptic surfaces yields families of elliptic K3 surfaces with various nonzero Mordell-Weil ranks. We also determined the global structures of the gauge groups that arise in F-theory compactifications on the resulting K3 surfaces times a K3 surface. U(1) gauge fields arise in these compactifications.

A bstract We construct six-dimensional (6D) F-theory models in which discrete ℤ 5 , ℤ 4 , ℤ 3 , and ℤ 2 gauge symmetries arise. We demonstrate that a special family of “Fano 3-folds” is a useful tool for constructing the aforementioned models. The geometry of Fano 3-folds in the constructions of models can be useful for understanding discrete gauge symmetries in 6D F-theory compactifications. We argue that the constructions of the aforementioned models are applicable to Calabi-Yau genus-one fibrations over any base space, except models with a discrete ℤ 5 gauge group. We construct 6D F-theory models with a discrete ℤ 5 gauge group over the del Pezzo surfaces, as well as over ℙ 1 × ℙ 1 and ℙ 2 . We also discuss some applications to four-dimensional F-theory models with discrete gauge symmetries.

A bstract We examine the proposal in the previous paper to resolve the puzzle in transitions in discrete gauge groups. We focus on a four-section geometry to test the proposal. We observed that a discrete ℤ 2 gauge group enlarges and U(1) also forms in F-theory along any bisection geometries locus in the four-section geometry built as the complete intersections of two quadrics in ℙ 3 fibered over any base. Furthermore, we demonstrate that giving vacuum expectation values to hypermultiplets breaks the enlarged U(1) × ℤ 2 gauge group down to a discrete ℤ 4 gauge group via Higgsing. We thus confirmed that the proposal in the previous paper is consistent when a four-section splits into a pair of bisections in the four-section geometry. This analysis may be useful for understanding the Higgsing processes occurring in the transitions in discrete gauge groups in six-dimensional F-theory models. We also discuss the construction of a family of six-dimensional F-theory models in which U(1) × ℤ 4 forms.

A bstract In this study, we introduce a new class of rational elliptic 3-folds, which we refer to as “1/2 Calabi-Yau 3-folds”. We construct elliptically fibered Calabi-Yau 3-folds by utilizing these rational elliptic 3-folds. The construction yields a novel approach to build elliptically fibered Calabi-Yau 3-folds of various Mordell-Weil ranks. Our construction of Calabi-Yau 3-folds can be considered as a three-dimensional generalization of the operation of gluing pairs of 1/2 K3 surfaces to yield elliptic K3 surfaces. From one to seven U(1)s form in six-dimensional N = 1 F-theory on the constructed Calabi-Yau 3-folds. Seven tensor multiplets arise in these models.

A bstract F-theory/heterotic duality is formulated in the stable degeneration limit of a K3 fibration on the F-theory side. In this note, we analyze the structure of the stable degeneration limit. We discuss whether stable degeneration exists for pairs of rational elliptic surfaces. We demonstrate that, when two rational elliptic surfaces have an identical complex structure, stable degeneration always exists. We provide an equation that systematically describes the stable degeneration of a K3 surface into a pair of isomorphic rational elliptic surfaces. When two rational elliptic surfaces have different complex structures, whether their sum glued along a smooth fiber admits deformation to a K3 surface can be determined by studying the structure of the K3 lattice. We investigate the lattice theoretic condition to determine whether a deformation to a K3 surface exists for pairs of extremal rational elliptic surfaces. In addition, we discuss the configurations of singular fibers under stable degeneration. The sum of two isomorphic rational elliptic surfaces glued together admits a deformation to a K3 surface, the singular fibers of which are twice that of the rational elliptic surface. For special situations, singular fibers of the resulting K3 surface collide and they are enhanced to a fiber of another type. Some K3 surfaces become attractive in these situations. We determine the complex structures and the Weierstrass forms of these attractive K3 surfaces. We also deduce the gauge groups in F-theory compactifications on these attractive K3 surfaces times a K3. E 6 , E 7 , E 8 , SU(5), and SO(10) gauge groups arise in these compactifications.

Abstract In this study, we introduce a new class of rational elliptic 3-folds, which we refer to as “1/2 Calabi-Yau 3-folds”. We construct elliptically fibered Calabi-Yau 3-folds by utilizing these rational elliptic 3-folds. The construction yields a novel approach to build elliptically fibered Calabi-Yau 3-folds of various Mordell-Weil ranks. Our construction of Calabi-Yau 3-folds can be considered as a three-dimensional generalization of the operation of gluing pairs of 1/2 K3 surfaces to yield elliptic K3 surfaces. From one to seven U(1)s form in six-dimensional N = 1 F-theory on the constructed Calabi-Yau 3-folds. Seven tensor multiplets arise in these models.

A bstract We determine the discrete gauge symmetries that arise in F-theory compactifications on examples of genus-one fibered Calabi-Yau 4-folds without a section. We construct genus-one fibered Calabi-Yau 4-folds using Fano manifolds, cyclic 3-fold covers of Fano 4-folds, and Segre embeddings of products of projective spaces. Discrete ℤ 5 , ℤ 4 , ℤ 3 and ℤ 2 symmetries arise in these constructions. We introduce a general method to obtain multisections for several constructions of genus-one fibered Calabi-Yau manifolds. The pullbacks of hyperplane classes under certain projections represent multisections to these genus-one fibrations. We determine the degrees of these multisections by computing the intersection numbers with fiber classes. As a result, we deduce the discrete gauge symmetries that arise in F-theory compactifications. This method applies to various Calabi-Yau genus-one fibrations.

A bstract We analyze four-dimensional (4d) N = 1 superconformal field theories (SCFTs) obtained as deformations of 4d N = 2 SCFTs on S-folds by tilting 7-branes. Geometric compatibility with the structures of S-folds constrains the forms of T-branes. As a result, brane monodromies are constrained. We also discuss two 4d N = 1 theories on probe D3-branes, where the two theories behave identically in IR, but they originate from different theories in UV. Studying the global structure of their geometry is useful in constructing these two theories.

In this study, non-electrically controlled SalivaDirect loop-mediated isothermal amplification (NEC-SD-LAMP), which can detect infections by amplifying viral DNA expression in saliva without using electrical control systems, was developed. By this method, only by adding water to the device, viral DNA was extracted from saliva using SalivaDirect, the extracted DNA was amplified via loop-mediated isothermal amplification (LAMP), and the results were visually confirmed. Melting palmitic acid maintained the optimal temperature for the LAMP reaction, as the temperature of palmitic acid is maintained at 62.9 °C, its melting point. By exploiting the proximity of the melting point to the optimal temperature for LAMP, LAMP can be performed without electricity. We detected several viruses in the saliva using this method. NEC-SD-LAMP could clearly distinguish 3 types of viral DNA, indicating the high specificity of this reaction. Furthermore, the viral concentration detection limit of the device was 2 copies per µL, indicating that it is possible to detect DNA viral infections in saliva even before the onset of viral infection.