Resumen de Aspects of T-branes
This thesis explores the BPS-stability of T-brane con gurations of 7-branes including -corrections as well as stability on compact 4-cycles in the absence of defects and including them.
First, we study '-corrections in multiple D7-brane con gurations with noncommuting pro les for their transverse position elds. We focus on T-brane systems, crucial in F-theory GUT model building. There 0-corrections modify the D-term piece of the BPS equations which, already at leading order, require a non-primitive Abelian worldvolume ux background. We nd that 0-corrections may either i) leave this ux background invariant, ii) modify the Abelian non-primitive ux pro le, or iii) deform it to a non-Abelian pro le.
The last case typically occurs when primitive uxes, a necessary ingredient to build 4d chiral models, are added to the system. We illustrate these three cases by solving the 0-corrected D-term equations in explicit examples, and describe their appearance in more general T-brane backgrounds. Finally, we discuss implications of our ndings for F-theory GUT local models.
Secondly, we analyse global aspects of 7-brane backgrounds with a noncommuting pro le for their worldvolume scalars, also known as T-branes. In particular, we consider con gurations with no poles and globally well-de ned over a compact Kähler surface. We nd that such T-branes cannot be constructed on surfaces of positive or vanishing Ricci curvature. For the existing T-branes, we discuss their stability as we move in Kähler moduli space at large volume and provide examples of T-branes splitting into non-mutually-supersymmetric constituents as they cross a stability wall.
Lastly, we consider the e ects of defects on the stability of T-brane systems.
Such defects are induced by the presence of 7-branes on additional four-cycles intersecting the locus of the T-brane system. Coupling of the elds on both stacks modi es the BPS-equations and we nd that it allows for T-branes on four-cycles that do not allow for stable T-branes in absence of defects due to the topological obstructions mentioned before. One class of these solutions feature poles in the Higgs- eld pro le. By performing a Kaluza-Klein expansion we show that in four dimensions the presence of these poles translates to defect zero-modes giving a vev to KK-modes. Finally, by taking a suitable limit, we show that in the case of a self-intersecting four-cycle, the defect picture can be linked to an eight-dimensional Higgs- eld valued in a larger gauge algebra.
