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Résumé |
F-theory compactifications on elliptically fibered Calabi-Yau threefolds give rise
to six-dimensional N=(1,0) supergravity theories. Consistency of these theories
requires the cancellation of gravitational, gauge, and mixed anomalies, leading to
nontrivial algebraic relations between classical intersection data and enumerative
invariants associated with curve classes in the fiber. In this talk, I will show
that the Gromov-Witten theory of fiber curve classes is naturally encoded by
quasi-Jacobi forms, whose modular transformation properties determine the Green-
Schwarz anomaly cancellation conditions of the associated F-theory models. I will
further argue that, within this class of string compactifications, these anomaly
cancellation conditions follow automatically from the holomorphic anomaly
equations of topological string theory. |
