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.
Highlights
We study α’-corrections in multiple D7-brane configurations with noncommuting profiles for their transverse position fields
We focus on T-brane systems, crucial in F-theory GUT model building
As follows from the scheme introduced in [14,15,16,17], in F-theory GUT models Yukawa couplings are computed in terms of a 7-brane super Yang-Mills theory with a nonAbelian group G, a Higgs/transverse-position field Φ and a gauge vector A
Summary
With the two examples of the previous section in mind, let us describe how α corrections affect the D-term equations for more general kinds of T-branes. If we switch a background flux H along 12 for a generic ψh2×ol, some components of H will preserve the Ansatz (5.7), while others will force to consider a gauge transformation including non-Cartan generators E±, as discussed in appendix C. For arbitrary complex function γ and one-form η ∈ Ω(1,0) Such that we have more freedom to satisfy primitivity condition and Bianchi identity than in the previous cases. Is a linear combination of the two-forms (5.12) and (5.13) which satisfies the Bianchi identity and the primitivity condition at leading order This is precisely the flux component denoted as H2, explicitly shown to be compatible with the Abelian Ansatz (5.7) therein.
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