James Fullwood, HKU, Hong Kong

On tadpole relations via Verdier specialization

Abstract

S-duality between two regimes of string theory referred to as ‘F-theory’ and ‘type IIB’ predicts a linear relation among the Euler characteristic of an elliptic Calabi-Yau fourfold and the Euler characteristics of certain divisors in a particular Calabi-Yau threefold. Such relations are often referred to in the physics literature as ‘tadpole relations’. It has been found that these tadpole relations coming from the equivalence between F-theory and type IIB may be shown to hold by integrating Chern class identities which hold in a much broader context than physical one. In this talk, using the construct of Verdier specialization we give a top-down explanation for the existence of such Chern class identities, yielding a purely mathematical explanation of the aforementioned tadpole relations predicted by physicists.