F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds

By D. Morrison, D. S. Park. 2012

235 citations recorded by the source corpus.

A bstractThe Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X contains information about the abelian sector of the six-dimensional theory obtained by compactifying F-theory on X. After examining features of the abelian anomaly coefficient matrix and U(1) charge quantization conditions of general F-theory vacua, we study CalabiYau threefolds with Mordell-Weil rank-one as a first step towards understanding the features of the Mordell-Weil group of threefolds in more detail. In particular, we generate an interesting class of F-theory models with U(1) gauge symmetry that have matter with both charges 1 and 2. The anomaly equations — which relate the Néron-Tate height of a section to intersection numbers between the section and fibral rational curves of the manifold — serve as an important tool in our analysis.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a708105d2bdeff150c016cac08e2c750d559de5c

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Citations in the corpus

Geometric engineering in toric F-theory and GUTs with U(1) gauge factors (2013, background): “Studying global U(1) symmetries is a topic of intense current research [11, 12, 13, 14, 15, 16, 17, 18, 19].”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “The divisor classes that support Abelian gauge fields in F-theory [34,39,77], see also [22,31,78], are obtained from the Shioda map σ of the rational sections ŝm.”
MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND F-THEORY: A REVIEW (2012, background): “An additional section was also studied without an SU(5) singularity in [190] where the general form of a 2-section model was presented.”
U(1) symmetries in F-theory GUTs with multiple sections (2012, methodology): “Let us stress that in section 5 we will provide a rather different resolution of the factorised Tate models based on a P1,1,2[4]-fibration that had appeared before in [11].”
Anomaly cancellation and abelian gauge symmetries in F-theory (2012, methodology): “The Shioda map has been applied for the construction of U(1)-symmetries in six-dimensional F-theory compactifications [5, 22, 23, 24] on elliptically fibered Calabi-Yau threefolds with rational sections.”
F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections (2013, methodology): “This parametrization will prove useful in the discussion of matter with only charge 1 under the Abelian gauge field corresponding to the rational point Q [43], i.”