Supersymmetric-field theory remains the best new physics beyond the SM and also "builds a bridge between the low energy phenomenology and high-energy fundamental physics". Moreover, I will show here that SuSy can incorporate aspects of loop quantum gravity to shed deep light on fundamental issues in quantum cosmology. Before getting deep, recall that the central action for supersymmetric field theory is:

with $\left| {_G} \right.$ the Grassmannian variable and total action is given by:

and the super-field/anti-super-field theory expansion in the Landau type gauge is given by:

with the super-covariant derivatives of

are defined by:

and

and the super-derivative is:

where the Ashtekar-Barbero connection $K_a^i$, for a, b = 1, 2, 3, is given in terms of co-triads $e_a^i$:

and $e_a^i$ satisfying

and the extrinsic curvature ${K_{ab}}$ being:

For definitions of terms, see my 'SuperSymmetric Field Theory and the Quantum Master Equation' post. Some philosophical points are in order first.

0

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 $\iota \Phi$ the inclusion of the complex Higgs field $\Phi$, and $S$ representing the symmetrization over gauge indices.

Locally, the Higgs field is given by:

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

with:

a Kähler coordiante expansion of $\gamma$ 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 $\lambda$, entailing that the F-term conditions are purely topological and in no need for $\alpha '$-corrections