I last introduced T-branes, which are non-Abelian deformation of intersecting D-brane systems in the corresponding compactification manifold. Then I showed that we have a Kähler-equivalence of the derivatives in the pull-back with the gauge-covariant ones, which gave us:

with the inclusion of the complex Higgs field , and representing the symmetrization over gauge indices.

Locally, the Higgs field is given by:

where is a matrix in the complexified adjoint representation of and its Hermitian conjugate. Thus, I could derive:

with:

a Kähler coordiante expansion of and gives us, after inserting it in:

the following:

which is the exact 7-brane superpotential for F-theory and the integrand is independent of , entailing that the F-term conditions are purely topological and in no need for -corrections

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