Algebraic cycles and local anomalies in F-theory

作者：Bies Martin^*; Mayrhofer Christoph; Weigand Timo

来源：The Journal of High Energy Physics, 2017, 2017(11): 100.

DOI：10.1007/JHEP11(2017)100

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

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.

• 出版日期2017-11-16