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

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.

23 pages

References in corpus (5)

• GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• Yukawa Structure from U(1) Fluxes in F-theory Grand Unification
• Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications
• Yukawas and discrete symmetries in F-theory compactifications without section

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• Discrete gauge groups in certain F-theory models in six dimensions
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• F-theory models on K3 surfaces with various Mordell-Weil ranks -constructions that use quadratic base change of rational elliptic surfaces
• Tools for CICYs in F-theory
• K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• Structure of stable degeneration of K3 surfaces into pairs of rational elliptic surfaces
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• A note on transition in discrete gauge groups in F-theory