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. |