Algebraic description of G-flux in F-theory: new techniques for F-theory phenomenology

TL;DR

This paper introduces algebraic methods to describe G-flux in F-theory, enabling direct computation of D3-tadpoles and chiral spectra, and confirms consistency with perturbative string theory in the weak coupling limit.

Contribution

It develops a comprehensive algebraic framework for G-flux in F-theory, facilitating calculations relevant to phenomenology and providing explicit examples.

Findings

Consistent G-flux calculations with type IIB in the weak coupling limit

Explicit algebraic techniques for D3-tadpole and chiral state computations

Applicability of methods to concrete F-theory models

Abstract

We give a global algebraic description of the four-form flux in F-theory. We present how to compute its D3-tadpole and how to calculate the number of four-dimensional chiral states at the intersection of 7-branes directly in F-theory. We check that, in the weak coupling limit, we obtain the same results as using perturbative type IIB string theory. We develop these techniques in full generality. However, they can be readily applied to concrete models, as we show in an explicit example.