T-Branes at the Limits of Geometry

TL;DR

The paper develops a geometric framework in which T-branes in 6D F-theory compactifications are described by Hitchin-like systems with singular Higgs fields, including irregular (wild) poles. By interpreting localized matter as sources for the Hitchin equations, higher-order poles arise from non-reduced schemes, and their moduli couple to closed-string deformations of the local Calabi–Yau geometry, enabling a unified description of both simple and wild Hitchin systems. Physical constraints such as anomaly cancellation and gravity decoupling impose bounds on the total matter content and pole orders, while gauge-singlet moduli in global F-theory models tune these poles, unifying disparate wild Higgs-bundle configurations within a single framework. The authors illustrate the construction with explicit SU(2) examples, analyze moduli spaces of wild Hitchin systems, and discuss extensions to global geometries and heterotic duals, highlighting the broader implications for open/closed string duality and Yukawa coupling phenomenology. The work provides a concrete bridge between Hitchin moduli and Calabi–Yau complex structure data, offering tools to explore Stokes data and isomonodromic deformations in a string-theoretic setting.

Abstract

Singular limits of 6D F-theory compactifications are often captured by T-branes, namely a non-abelian configuration of intersecting 7-branes with a nilpotent matrix of normal deformations. The long distance approximation of such 7-branes is a Hitchin-like system in which simple and irregular poles emerge at marked points of the geometry. When multiple matter fields localize at the same point in the geometry, the associated Higgs field can exhibit irregular behavior, namely poles of order greater than one. This provides a geometric mechanism to engineer wild Higgs bundles. Physical constraints such as anomaly cancellation and consistent coupling to gravity also limit the order of such poles. Using this geometric formulation, we unify seemingly different wild Hitchin systems in a single framework in which orders of poles become adjustable parameters dictated by tuning gauge singlet moduli of the F-theory model.

Figures (6)

• Figure 1: Depiction of a Hitchin system on a genus one curve with poles at marked points indicated by narrow cylindrical regions, that is, spikes. Background values for localized matter fields induce poles in the Higgs field of the Hitchin system. On the left we depict matter localized at $u = p$ which generates a simple pole. On the right we depict matter localized at the non-reduced scheme $(u-q)^k = 0$ which generates a higher order pole.
• Figure 2: Depiction of the star shaped quiver generated by an intersecting brane configuration in F-theory. The central node corresponds to the contribution from the 7-brane wrapped over the gauge theory curve, and the satellite nodes indicated as squares correspond to the flavor branes of the system. These intersect the Hitchin system curve at points, and for $k$ such intersecting fields, there are regions in the moduli space which are represented by higher poles in the Hitchin system Higgs field. Each such satellite node corresponds to the location of a distinct marked point.
• Figure 3: Stokes rays, and Stokes Sectors and Super Sectors
• Figure 4: Anti-Stokes directions.
• Figure 5: Data needed to define a tentacle.

Theorems & Definitions (17)

• Definition A.1
• Definition A.2
• Definition A.3
• Remark A.4
• Definition A.5
• Remark A.6: Parameter space
• Definition A.7
• Remark A.8
• Remark A.9
• Remark A.10