Article quick-view

Research paper by

Mboyo Esole, Monica Jinwoo Kang, Shing-Tung Yau

Indexed on

30th Sep 2014

Published on

30th Sep 2014

Published in

High Energy Physics - Theory

This paper is not available for free

You can find the original article on the journal website.

Go to sourceWe introduce a new model for elliptic fibrations endowed with a Mordell-Weil group of rank one. We call it a Q$_7(\mathscr{L},\mathscr{S})$ model. It naturally generalizes several previous models of elliptic fibrations popular in the F-theory literature. The model is also explicitly smooth, thus relevant physical quantities can be computed in terms of topological invariants in straight manner. Since the general fiber is defined by a cubic curve, basic arithmetic operations on the curve can be done using the chord-tangent group law. We will use this model to determine the spectrum of singular fibers of an elliptic fibration of rank one and compute a generating function for its Euler characteristic. With a view toward string theory, we determine a semi-stable degeneration which is understood as a weak coupling limit in F-theory. We show that it satisfies a non-trivial topological relation at the level of homological Chern classes. This relation ensures that the D3 charge in F-theory is the same as the one in the weak coupling limit.