T-branes and $\alpha'$-corrections

TL;DR

This paper investigates how $oldsymbol{ extalpha'}$-corrections influence T-brane configurations in F-theory, revealing that these corrections can alter flux backgrounds and potentially induce non-Abelian profiles, impacting GUT model building.

Contribution

It provides a detailed analysis of $oldsymbol{ extalpha'}$-corrections in T-branes, showing their effects on flux backgrounds and the emergence of non-Abelian profiles in F-theory GUT models.

Findings

$oldsymbol{ extalpha'}$-corrections modify D-term equations in T-branes.

Corrections can leave flux backgrounds invariant, modify Abelian flux, or induce non-Abelian profiles.

Explicit solutions illustrate the different effects of $oldsymbol{ extalpha'}$-corrections.

Abstract

We study $\alpha'$-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 $\alpha'$-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 $\alpha'$-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 $\alpha'$-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.