Lectures on F-theory compactifications and model building

By T. Weigand. 2010

262 citations recorded by the source corpus.

These lecture notes are devoted to formal and phenomenological aspects of F-theory. We begin with a pedagogical introduction to the general concepts of F-theory, covering classic topics such as the connection to type IIB orientifolds, the geometry of elliptic fibrations and the emergence of gauge groups, matter and Yukawa couplings. As a suitable framework for the construction of compact F-theory vacua we describe a special class of Weierstrass models called Tate models, whose local properties are captured by the spectral cover construction. Armed with this technology we proceed with a survey of F-theory grand unified theory (GUT) models, aiming at an overview of basic conceptual and phenomenological aspects, in particular in connection with GUT breaking via hypercharge flux.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a3ef4ef05bce57dab63d6057fa06a05e496a6d50

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Citations in the corpus

The Swampland: Introduction and Review (2019, result): “We refer to [289–291] for some reviews on this uplift.”
Matter and singularities (2011, methodology): “F-theory methods for analyzing matter in 4D theories in the presence of flux were developed in [24, 25]; following these works there has been a great deal of recent work on 4D F-theory constructions with particular focus on phenomenological applications (see for example [40, 41, 42, 43]); for review”
F-theory fluxes, chirality and Chern-Simons theories (2011, methodology): “Geometrically this corresponds to a degeneration of the elliptic fiber over divisors in the base wrapped by the seven-branes [1, 2].”
Geometric engineering in toric F-theory and GUTs with U(1) gauge factors (2013, background): “While the original models were local, and thus decoupled from gravity, vast progress has been made in the search for global realizations [3, 4, 5, 6, 7, 8, 9, 10].”
U(1) symmetries in F-theory GUTs with multiple sections (2012, background): “In F-theory [5–9] gauge symmetries are geometric in origin and so understanding the geometry associated to U(1) symmetries is crucial to this aspect of model building.”
T-branes and monodromy (2010, background): “When three seven-branes intersect, the fields living at the three (1)See [5, 6] for recent reviews.”
Explicit de Sitter flux vacua for global string models with chiral matter (2013, background): “Similarly local F-theory models provide another interesting class of models with realistic properties [6, 11–14].”
D-branes at del Pezzo singularities: global embedding and moduli stabilisation (2012, methodology): “• Quasi realistic local models have been constructed from D-branes at singularities [2– 9] and from F-theory constructions (for a review see [10–12]).”
F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections (2013, background): “Our understanding of both the local approach as well its embedding into global compactifications has improved vastly over the last years [10, 11, 12].”
MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND F-THEORY: A REVIEW (2012, background): “There are a number of nice reviews of the formalism relating F-theory and 7-branes which we refer to for any further details required [17,167–171].”
Anomaly equations and intersection theory (2011, background): “A nice review of this subject and further references can be found in [85].”
Top down approach to 6D SCFTs (2018, background): “Some resources for additional background can be found for example in the book [84], and in the context of particle physics model building applications in references [85,86].”
G-flux in F-theory and algebraic cycles (2011, background): “In F-theory, both kinds of fluxes are encoded in a four-form flux G4 on X4 (see also [14, 15]).”
Yukawas, G-flux, and spectral covers from resolved Calabi-Yau’s (2011, background): “The interested reader is referred to the sizeable literature in [49] and references contained therein.”