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Although Supersymmetry (SUSY) - under certain assumptions - predicts the existence of Dark Matter (DM) candidate, the signals for DM are not specific to SUSY. Fist, how to detect DM at the LHC: DM will not be detected by the experiments directly as it is believed (reasonable assumption) to not interact with regular matter. Therefore the only way of ...


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Weyl Invariance in 8d, Majorana invariance in 9D and no reductions are possible in 7D. So the minimum number of supercharges in 8,9D = $2^{8/2}/2$ complex components = 16 real supercharges. And in 7D that number is $2^{6/2}$ complex components = 16 real supercharges For further details, refer to the appendix of Polchinski vol 2


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Hint: Think of way to write the Hamiltonian as $$\hat{H}~=~ -\frac{\hbar^2}{2m}\frac{d^2}{dx^2} +V(x)~=~\hat{B}^{\dagger}\hat{B} ~\geq~0 $$ for some first-order differential operator $$\hat{B}~=~a(x)\frac{d}{dx} +b(x) ,$$ with suitable functions $a(x)$ and $b(x)$. Here the potential $V(x)$ is given by formula (1). Can you see what the operator ...



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