Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications

Abstract

We study F-Theory compactifications to four dimensions that exhibit discrete gauge symmetries. Geometrically these arise by deforming elliptic fibrations with two sections to a genus-one fibration with a bi-section. From a four-dimensional field-theory perspective they are remnant symmetries from a Higgsed U(1) gauge symmetry. We implement such symmetries in the presence of an additional SU(5) symmetry and associated matter fields, giving a geometric prescription for calculating the induced discrete charge for the matter curves and showing the absence of Yukawa couplings that are forbidden by this charge. We present a detailed map between the field theory and the geometry, including an identification of the Higgs field and the massless states before and after the Higgsing. Finally we show that the Higgsing of the U(1) induces a G-flux which precisely accounts for the change in the Calabi-Yau Euler number so as to leave the D3 tadpole invariant.

30 pages; v2: substantially improved presentation, refs added; v3: refs. added, appendix A on remnant discrete subgroups included; v4: refs. added

References in corpus (12)

• Symmetries and Strings in Field Theory and Gravity
• Lectures on F-theory compactifications and model building
• Les Houches Lectures on Constructing String Vacua
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• D-brane Deconstructions in IIB Orientifolds
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• Yukawas and discrete symmetries in F-theory compactifications without section
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Tate Trees for Elliptic Fibrations with Rank one Mordell-Weil group
• A Heterotic Standard Model with B-L Symmetry and a Stable Proton
• Discrete Family Symmetry from F-Theory GUTs

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• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Rigour and Rigidity: Systematics on particle physics D6-brane models on Z(2)xZ(6)
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• Complete Intersection Fibers in F-Theory
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• Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification (String Math 2022 Proceedings)
• Root bundles: Applications to F-theory Standard Models
• New perspectives in the duality of M-theory, heterotic strings, and F-theory