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Article
Report number	arXiv:1706.08528
Title	Algebraic Cycles and Local Anomalies in F-Theory
Related title	Algebraic Cycles and Local Anomalies in F-Theory
Author(s)	Bies, Martin (U. Heidelberg, ITP) ; Mayrhofer, Christoph (Munich U., ASC) ; Weigand, Timo (U. Heidelberg, ITP ; CERN)
Publication	2017-11-16
Imprint	2017-06-26
Number of pages	45
Note	45 pages
In:	JHEP 11 (2017) 100
DOI	10.1007/JHEP11(2017)100
Subject category	hep-th ; Particle Physics - Theory
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.
Copyright/License	arXiv nonexclusive-distrib. 1.0

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