Enhancements in F-theory models on moduli spaces of K3 surfaces with ADE rank 17

Abstract

We study the moduli of elliptic K3 surfaces with a section with the ADE rank 17. While the Picard number of a generic K3 surface in such moduli space is 19, the Picard number is enhanced to 20 at special points in the moduli. K3 surfaces become attractive K3 surfaces at these points. Either of the following two situations occurs at such special points: i) the Mordell-Weil rank of an elliptic K3 surface is enhanced, or ii) the gauge symmetry is enhanced. The first case i) is related to the appearance of a U (1) gauge symmetry. In this note, we construct the moduli of K3 surfaces with ADE types E 7 D 10 and A 17 . We determine some of the special points at which K3 surfaces become attractive in the moduli of K3 surfaces with ADE types E 7 D 10 and A 17 . We investigate the gauge symmetries in F-theory compactifications on attractive K3 surfaces which correspond to such special points in the moduli times a K3 surface. U (1) gauge symmetry arises in some F-theory compactifications. arXiv:1712.08539v3 [hep-th]

F-theory models with U(1) × ℤ2, ℤ4 and transitions in discrete gauge groups

“…3 See, e.g. [48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76] for discussions of F-theory on elliptic fibrations with a global section. 4 When F-theory is compactified on a Calabi-Yau genus-one fibration Y , the discrete gauge group arising in this compactification is identified with the discrete part of the "Tate-Shafarevich group," X(J(Y )), of the Jacobian, J(Y ) [47,19].…”

Discrete gauge groups in certain F-theory models in six dimensions

“…This formulation enables the axiodilaton to admit an SL 2 (Z) monodromy. F-theory compactifications on elliptic fibrations with a global section have previously been analyzed [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]. Furthermore, the physical interpretation of F-theory compactification on a genus-one fibration without a section was recently discussed in [30,31].…”

$$ \frac{1}{2} $$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s

“…The rank of the group formed by the set of the global sections of the compactification space -or the "Mordell-Weil group"-yields the number of U (1) factors forming in F-theory on the space [3]. The rank 1 Recent studies of F-theory models on elliptic fibrations that admit a global section can be found, for example, 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].…”