Anomaly cancellation and abelian gauge symmetries in F-theory

By M. Cvetič, Thomas W. Grimm, Denis Klevers. 2012

139 citations recorded by the source corpus.

A bstractWe study 4D F-theory compactifications on singular Calabi-Yau fourfolds with fluxes. The resulting $\mathcal{N}=1$ effective theories can admit non-Abelian and U(1) gauge groups as well as charged chiral matter. In these setups we analyze anomaly cancellation and the generalized Green-Schwarz mechanism. This requires the study of 3D $\mathcal{N}=2$ theories obtained by a circle compactification and their M-theory duals. Reducing M- theory on resolved Calabi-Yau fourfolds corresponds to considering the effective theory on the 3D Coulomb branch in which certain massive states are integrated out. Both 4D gaugings and 3D one-loop corrections of these massive states induce Chern-Simons terms. All 4D anomalies are captured by the one-loop terms. The ones corresponding to the mixed gauge-gravitational anomalies depend on the Kaluza-Klein vector and are induced by integrating out Kaluza-Klein modes of the U(1) charged matter. In M-theory all Chern-Simons terms classically arise from G4-flux. We find that F-theory fluxes implement automatically the 4D Green-Schwarz mechanism if non-trivial geometric relations for the resolved Calabi-Yau fourfold are satisfied. We confirm these relations in various explicit examples and elucidate the general construction of U(1) symmetries in F-theory. We also compare anomaly cancellation in F-theory with its analog in Type IIB orientifold setups.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/cba4e1a9e9cb163aebc8c4dc01a8b50101add9b7

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

U(1) symmetries in F-theory GUTs with multiple sections (2012, background): “Indeed a lot of recent progress has been made towards understanding the explicit construction and fully global aspects of U(1)s in four-dimensional F-theory compactifications [4, 5, 6, 7, 8, 9, 10] and in compactifications to six dimensions [11].”
MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND F-THEORY: A REVIEW (2012, background): “2 were for the weakly coupled IIB limit it is reasonable to expect that similar reasoning applies to their F-theoretic uplift, as studied in [166].”
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].”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “6) of vertical divisors enter the coefficients of the Green-Schwarz terms [22, 34, 35] and are thus essential for anomaly cancellation, cf.”
F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections (2013, methodology): “It is defined as the map from the Mordell-Weil group to H((1,1))(X̂) given by [43, 55, 44] σ(ŝm) := Sm − S̃P − (Sm · S̃P ·Dα)ηDβ + ∑”