Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds

Abstract

In this study, we analyze gauge groups in six-dimensional N = 1 F-theory models. We construct elliptic Calabi-Yau 3-folds possessing various singularity types as double covers of "1/2 Calabi-Yau 3-folds", a class of rational elliptic 3-folds, by applying the method discussed in a previous study to classify the singularity types of the 1/2 Calabi-Yau 3-folds. One to three U(1) factors are formed in six-dimensional F-theory on the constructed Calabi-Yau 3folds. The singularity types of the constructed Calabi-Yau 3-folds corresponding to the non-Abelian gauge group factors in six-dimensional F-theory are deduced. The singularity types of the Calabi-Yau 3-folds constructed in this work consist of A-and D-type singularities.

Singularities of 1/2 Calabi-Yau 4-folds and classification scheme for gauge groups in four-dimensional F-theory

“…The resulting structure of the singular fiber is given by three P 1 s, any pair of which meet at one point; that is, a type I 3 fiber. The situation is analogous to the appearance of the type I 3 fiber described in [47].…”

“…F-theory models of elliptic fibrations possessing a global section have been analyzed. Recent studies of such models can be found, e.g., in[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]. F-theory model constructions where one or more U(1) factors are formed are discussed, for example, in[4,7,8,10,…”

“…The matrix representation of a cubic hypersurface in P 3 need not be symmetric, whereas the matrix representation of a quartic plane curve as the dual of a 1/2 Calabi-Yau 3-fold[45,47] must be symmetric.…”