Gauge Groups and Matter Fields on Some Models of F-theory without Section

TL;DR

This paper explores F-theory compactifications on elliptic Calabi-Yau 4-folds without sections, constructed from special elliptic K3 surfaces, revealing gauge groups without U(1) factors and the emergence of E6 in some models.

Contribution

It introduces a method to build elliptic Calabi-Yau 4-folds without sections using elliptic K3 surfaces and analyzes the resulting gauge groups and matter fields in F-theory.

Findings

Gauge groups without U(1) factors are realized on 7-branes.

Exceptional group E6 appears in some models.

Constructed models expand understanding of F-theory without sections.

Abstract

We investigate F-theory on an elliptic Calabi-Yau 4-fold without a section to the fibration. To construct an elliptic Calabi-Yau 4-fold without a section, we introduce families of elliptic K3 surfaces which do not admit a section. A product K3 $\times$ K3, with one of the K3's chosen from these families of elliptic K3 surfaces without a section, realises an elliptic Calabi-Yau 4-fold without a section. We then compactify F-theory on such K3 $\times$ K3's. We determine the gauge groups and matter fields which arise on 7-branes for these models of F-theory compactifications without a section. Since each K3 $\times$ K3 constructed does not have a section, gauge groups arising on 7-branes for F-theory models on constructed K3 $\times$ K3's do not have $U(1)$-part. Interestingly, exceptional gauge group $E_6$ appears for some cases.