T-branes are supersymmetric intersecting brane configurations such that the non-Abelian Higgs field that describes D-brane deformations is not diagonalisable and satisfies nilpotency conditions where the worldvolume flux has non-commuting expectation values and their worldvolume adjoint Higgs field is given a VEV that cannot be captured by its characteristic polynomial, and thus derive their importance from the fact that heterotic string compactifications are dual to T-branes in F-theory. Let’s probe their dynamics. Starting with the D-term potential:

with the -charge:

and the gauge flux that yields the Fayet-Iliopoulos term:

where the D-brane partition function for closed strings is given by:

with a non-Abelian D-term: