F-theory fluxes, chirality and Chern-Simons theories

By Thomas W. Grimm, Hirotaka Hayashi. 2011

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A bstractWe study the charged chiral matter spectrum of four-dimensional F-theory compactifications on elliptically fibered Calabi-Yau fourfolds by using the dual M-theory description. A chiral spectrum can be induced by M-theory four-form flux on the fully resolved Calabi-Yau fourfold. In M-theory this flux yields three-dimensional Chern-Simons couplings in the Coulomb branch of the gauge theory. In the F-theory compactification on an additional circle these couplings are only generated by one-loop corrections with charged fermions running in the loop. This identification allows us to infer the net number of chiral matter fields of the four-dimensional effective theory. The chirality formulas can be evaluated by using the intersection numbers and the cones of effective curves of the resolved fourfolds. We argue that a study of the effective curves also allows to follow the resolution process at each co-dimension. To write simple chirality formulas we suggest to use the effective curves involved in the resolution process to determine the matter surfaces and to connect with the group theory at co-dimension two in the base. We exemplify our methods on examples with SU(5) and SU(5) × U(1) gauge group.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/87ad258e485c34063b1e5ad616b684baf8622cd9

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In Nuclear and High Energy Physics

Citations in the corpus

MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND F-THEORY: A REVIEW (2012, methodology): “The state of the art there are models which exhibit 3 chiral generations, though none have a fully realistic Higgs sector: the models of [179,180] do not consider doublet-triplet splitting and in [182] Wilson lines are utilised though with results yielding multiple Higgs fields.”
F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections (2013, background): “Rank one Mordell-Weil groups in compact elliptic fibrations have been studied recently in the F-theory literature in varying contexts [39, 40, 41, 42, 43, 44, 45, 46].”
Anomaly equations and intersection theory (2011, methodology): “A convenient method to investigate the abelian sector of F-theory backgrounds is to use M-theory/F-theory duality [7], and take an intersection theory-based2 approach in the dual M-theory background [10, 13, 23, 24, 25, 26].”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “• Elliptic fibers with an increasing number of rational points and their corresponding elliptically fibered Calabi-Yau manifolds X with a Mordell-Weil group (MW-group) of rational sections of increasing rank have been systematically constructed and studied [31–46].”
Anomaly cancellation and abelian gauge symmetries in F-theory (2012, methodology): “They shrink to zero in the blow-down X̂4 → X4 and constitute the generators of the relative Mori cone [71, 6], the complement of the Mori cone of X4 in X̂4.”
U(1) symmetries in F-theory GUTs with multiple sections (2012, methodology): “This resolution process has been studied with different techniques in the recent F-theory SU(5) GUT literature in a number of papers [22, 23, 24, 6, 7, 8] (see [25] for other gauge groups) and we use the process described in [6, 8].”
Geometric engineering in toric F-theory and GUTs with U(1) gauge factors (2013, methodology): “This can be done systematically by evaluating the three-dimensional Chern-Simons terms as in [48, 14, 16].”