Gauge Fluxes in F-theory and Type IIB Orientifolds

TL;DR

This work develops a detailed map between $G_4$ gauge fluxes in F-theory compactifications with $SU(n)$ and $SU(n)\times U(1)$ gauge symmetry and their Type IIB orientifold limits. By resolving the relevant Tate models, it classifies factorisable $G_4$-fluxes in the vertical subspace $H^{2,2}_{\rm vert}(\hat{Y}_4)$, and matches them to universal D5-tadpole-free $U(1)$-fluxes in Type IIB, identifying $G_4^{\lambda}$ with the universal spectral-cover flux (diagonal $U(1)$) and $G_4^{X}$ with a linear combination of brane fluxes. The Sen limit is analyzed with care to avoid conifold points, ensuring a consistent comparison and clarifying brane recombination between generic and $U(1)$-restricted Tate models. The results illuminate how perturbative Type IIB flux data reproduce and constrain global F-theory fluxes, including the realization of massive and massless $U(1)$ gauge factors and the associated D3- and D5-tadpoles, thus providing a concrete bridge between local spectral-cover intuition and global F-theory geometry.

Abstract

We provide a detailed correspondence between G_4 gauge fluxes in F-theory compactifications with SU(n) and SU(n)x(1) gauge symmetry and their Type IIB orientifold limit. Based on the resolution of the relevant F-theory Tate models we classify the factorisable G_4-fluxes and match them with the set of universal D5-tadpole free U(1)-fluxes in Type IIB. Where available, the global version of the universal spectral cover flux corresponds to Type IIB gauge flux associated with a massive diagonal U(1). In U(1)-restricted Tate models extra massless abelian fluxes exist which are associated with specific linear combinations of Type IIB fluxes. Key to a quantitative match between F-theory and Type IIB is a proper treatment of the conifold singularity encountered in the Sen limit of generic F-theory models. We also shed further light on the brane recombination process relating generic and U(1)-restricted Tate models.

Figures (3)

• Figure 1: Schematic drawing of the Calabi-Yau $X_3$ and its orientifold projection $\pi$ to $B$. The Calabi-Yau is embedded as a hypersurface in the $\mathcal{O}(\bar{\cal K})$-bundle over $B$.
• Figure 2: Brane configurations for \ref{['fig:non-restricted']}$SU(n)$- and \ref{['fig:restricted']}$SU(n)\times U(1)$- Type IIB set-ups. Note that $V$ and $\tilde{V}$ lie in the same class in the latter case if $n$ is even.
• Figure 3: Toric Lattice Polytope corresponding to the sub-manifold of the $SU(2)$-resolution manifold spanned by the coordinate sub-set $\{x, y, z, e_0, e_1\}$ (the lower red dot denotes the origin of the lattice)