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arXiv · 1706.08528

Algebraic Cycles and Local Anomalies in F-Theory

Martin Bies·Christoph Mayrhofer·Timo Weigand
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Abstract

We introduce a set of identities in the cohomology ring of elliptic fibrations which are equivalent to the cancellation of gauge and mixed gauge-gravitational anomalies in F-theory compactifications to four and six dimensions. The identities consist in (co)homological relations between complex codimension-two cycles. The same set of relations, once evaluated on elliptic Calabi-Yau three-folds and four-folds, is shown to universally govern the structure of anomalies and their Green-Schwarz cancellation in six- and four-dimensional F-theory vacua, respectively. We furthermore conjecture that these relations hold not only within the cohomology ring, but even at the level of the Chow ring, i.e. as relations among codimension-two cycles modulo rational equivalence. We verify this conjecture in non-trivial examples with Abelian and non-Abelian gauge groups factors. Apart from governing the structure of local anomalies, the identities in the Chow ring relate different types of gauge backgrounds on elliptically fibred Calabi-Yau four-folds.

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Martin Bies, Christoph Mayrhofer, Timo Weigand. 2017-06-26. Algebraic Cycles and Local Anomalies in F-Theory. https://doi.org/10.1007/jhep11(2017)100

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