Global tensor-matter transitions in F-theory

TL;DR

The paper develops a comprehensive framework for global tensor–matter transitions in six-dimensional F-theory compactifications, showing how tuning to (4,6,12) superconformal points and subsequent base blow-ups alter hyper- and tensor-multiplet sectors while preserving the gauge algebra. By leveraging anomalous constraint equations and the Green–Schwarz mechanism, the authors uniquely fix the non-Abelian matter changes and constrain Abelian charges, then realize and test these transitions in toric hypersurface models with explicit top constructions. They provide a complete classification across all semi-simple gauge algebras and illustrate multiple non-perturbative examples, including those with discrete symmetries, confirming the consistency with 6d anomalies and the geometric interpretation of SCPs as non-flat fibers. The work advances the understanding of the tensor branch and the landscape of 6d SUGRA vacua in F-theory, and suggests avenues for including singular divisors and more exotic matter in future studies.

Abstract

We use F-theory to study gauge algebra preserving transitions of 6d supergravity theories that are connected by superconformal points. While the vector multiplets remain unchanged, the hyper- and tensor multiplet sectors are modified. In 6d F-theory models, these transitions are realized by tuning the intersection points of two curves, one of them carrying a non-Abelian gauge algebra, to a (4,6,12) singularity, followed by a resolution in the base. The six-dimensional supergravity anomaly constraints are strong enough to completely fix the possible non-Abelian representations and to restrict the Abelian charges in the hypermultiplet sector affected by the transition, as we demonstrate for all Lie algebras and their representations. Furthermore, we present several examples of such transitions in torically resolved fibrations. In these smooth models, superconformal points lead to non-flat fibers which correspond to non-toric Kähler deformations of the torus-fibered Calabi-Yau 3-fold geometry.

Figures (10)

• Figure 1: Theories connected by a global tensor-matter transition.
• Figure 2: Resolution of SCPs in codimension-two.
• Figure 3: Schematic picture of the change in rational sections over blow-up divisors with gauge group $\overline{G} = \text{SU}(4) \times \text{U}(1)$.
• Figure 4: Summary of the two transitions. After tuning the complex structure of $Y_3$ to obtain $Y_{3,\text{sing}}$, we can either add another vertex $\mathfrak{f}$ to the top such that we get $k$ SCP points in $\hat{Y}_3$, or we can blowup the base $k$ times, which leads to $k$ new tensor multiplets in $\tilde{Y}_3$.
• Figure 5: The SU(3) top polytopes over $F_1$ before (upper figure) and after (lower figure) the transition. Simplified depictions of the polytope are shown on the left, where vertices at height one are drawn as blue circles and points internal to facets are drawn as filled blue circles. The toric blow-up by $\mathfrak{f}_3$ leaves the vertex $\mathbf{f_0}$ in a face.