The Equations we know of

First is General Relativity. The action can be put in this form: \[ S_{EH'}=\frac{1}{8\kappa}\int \sqrt{-g}\left( g^{ab}g^{de}g^{cf} +2 g^{ac}g^{bf}g^{de} + 3g^{ad}g^{be}g^{cf} -6 g^{ad}g^{bf}g^{ce} \right)\partial_c g_{ab}\partial_f g_{de} dx^4 \] Where \(g^{ab} = \frac{1}{4!}\varepsilon^{apqr}\varepsilon^{auvw}g_{pu}g_{qv}g_{rw} / \det(g) \)
We can get Maxwell's equations from the above by a Kaluza-Klein compactification on (D+n) dimensions. They are:  \[S_{YM} = \int\sqrt{-g}\frac{1}{2}(g^{ab}g^{cd} - g^{ac}g^{bd})(\partial_a A_b + i A_a A_b) (\partial_c A_d + i A_c A_d) dx^4 \] Where the A fields are matrices which generate the gauge group. Then Dirac's equations are: \[S_D = \int e \psi^\dagger e^a\sigma (\partial_a + i A_a.\tau + i\Omega_a)\psi + M (\psi \varepsilon\psi + \psi^\dagger \varepsilon\psi^\dagger )dx^4\] with: \[ \Omega_a = \varepsilon e_a e^b e^c \partial_b e_c \] and \(\tau\) is a generator of a gauge group, such as SU(n). M is a matrix which gives the masses. \(\psi\) is a collumn of particles. And \[\sigma.x = \begin{bmatrix} x+t & y+iz \\ y-iz & x-t\end{bmatrix} \] \[\varepsilon = \begin{bmatrix} 0 & 1 \\ -1 & 0\end{bmatrix} \] What we don't know: Why gauge group is \(SU(3)\times SU(2)\times U(1)\). Where the particle masses, CKM matrix and PMNS matrix gets their values. Finally there is a Higgs field: \[S_H = \int \sqrt{-g} \left(g^{ab}(\partial_a+iA_a) \phi (\partial_b +iA_b)\phi + V(\phi) \right)dx^4 \]

Supersymmetry

Super Yang mills in 10 dimensions for any gauge group G: \[ S = \int \operatorname{tr} \left\{ -\frac{1}{2} F_{ab} F^{ab} - i \psi^\alpha \gamma^a_{\alpha\beta} (\partial_a + ig A_a) \psi^\beta \right\} \] Supergravity in 11 dimensions: \[ S = \int \sqrt{-g} \left( R + F^{abcd}F_{abcd} -\frac{1}{6} \varepsilon^{abcdefghijk}A_{abc}F_{defg}F_{hijk}\right) dx^{11} \] \[ + \int \sqrt{-g} \left( \psi_a^\dagger \gamma^{abc} (\partial_b+i\Omega_b)\psi_c +(F_{abcd}+F^*_{abcd})(\psi^\dagger_e \gamma^{abcdef} \psi_f + 12 \psi^{\dagger a}\gamma^{bc} \psi^d) \right) dx^{11} \] With Supersymmetry (guessing): \[\delta A_{abc} = \gamma_{abcd}\psi^d \] \[\delta \psi^a = \gamma^{abcde}\partial_b A_{cde} + \gamma^{abc}\gamma^n \partial_b e^n_c\] \[\delta e^n_a = \gamma^n\psi_a \]