Journal of High Energy Physics

, 2017:100 | Cite as

Algebraic cycles and local anomalies in F-theory

  • Martin Bies
  • Christoph Mayrhofer
  • Timo Weigand
Open Access
Regular Article - Theoretical Physics


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.


Anomalies in Field and String Theories F-Theory Differential and Algebraic Geometry Flux compactifications 


Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikRuprecht-Karls-UniversitätHeidelbergGermany
  2. 2.Arnold Sommerfeld Center for Theoretical PhysicsMünchenGermany
  3. 3.CERN, Theory DivisionGeneva 23Switzerland

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