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Anomaly cancellation and abelian gauge symmetries in F-theory

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Abstract

We 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 G 4-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.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104-6396, U.S.A.

    Mirjam Cvetič & Denis Klevers

  2. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia

    Mirjam Cvetič

  3. Max-Planck-Institut für Physik, Föhringer Ring 6, 80805, Munich, Germany

    Thomas W. Grimm

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Cvetič, M., Grimm, T.W. & Klevers, D. Anomaly cancellation and abelian gauge symmetries in F-theory. J. High Energ. Phys. 2013, 101 (2013). https://doi.org/10.1007/JHEP02(2013)101

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