T-branes and $α'$-corrections

TL;DR

The paper investigates how ${\alpha}'$-corrections affect D7-brane systems with non-Abelian Higgs profiles, emphasizing T-branes in F-theory GUT contexts. It shows that holomorphic F-term data is protected, while D-term equations receive higher-order corrections that can preserve the background, modify Abelian flux, or necessitate non-Abelian flux backgrounds, depending on the flux content and supersymmetry. In eight-supercharge setups, backgrounds generally remain solutions; with four supercharges, corrections can qualitatively alter the flux configuration or require generalized complexified gauge transformations. The holomorphic Yukawa structures central to local F-theory models are robust under these corrections, though the detailed flux-induced normalizations and couplings may shift, informing future model-building and phenomenology.

Abstract

We study $α'$-corrections in multiple D7-brane configurations with non-commuting profiles for their transverse position fields. We focus on T-brane systems, crucial in F-theory GUT model building. There $α'$-corrections modify the D-term piece of the BPS equations which, already at leading order, require a non-primitive Abelian worldvolume flux background. We find that $α'$-corrections may either i) leave this flux background invariant, ii) modify the Abelian non-primitive flux profile, or iii) deform it to a non-Abelian profile. The last case typically occurs when primitive fluxes, a necessary ingredient to build 4d chiral models, are added to the system. We illustrate these three cases by solving the $α'$-corrected D-term equations in explicit examples, and describe their appearance in more general T-brane backgrounds. Finally, we discuss implications of our findings for F-theory GUT local models.