Aspects of T-branes

We explore the BPS-stability of T-brane configurations of 7-branes on compact 4-cycles in the absence of defects and including them. First, we consider configurations with no poles and globally well-defined over a compact Kähler surface. We find that such T-branes cannot be constructed on surfaces of positive or vanishing Ricci curvature. Secondly, we consider the effects 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 fields on both stacks modifies the BPS-equations and we find 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.