A question in four parts What are the main problems which supersymmetry purports to solve What would constitute lack of evidence for susy at the proposed lhc energy scales (e.g I don't understand what this means In strathdeee's extended poincare supersymmetry, the first entry on page 16 lists the massless multiplets of 6d $\\mathcal{n} = (1,0)$ supersymmetry as $2^2 = (2,1 4 supergravity by daniel z freedman and antoine van proeyen is quite excellent for illustrating clifford algebra techniques and calculations in the classical susy/sugra in general (in the component formalism)
The book has several calculations illustrated and plenty of exercises. So what is the general mathematical definition of bps states which is independent of the theory in consideration, say a general susy quantum field theories, be it qft, string theory, gravity and in any dimension. 1 this question already has answers here Number of supersymmetric charge and the meaning of $\cal n$ (2 answers) what's the $ {\cal n}$ for susy theories One of the advantages of supersymmetry in phenomenology is that the bosons and fermions cancel their quadratically divergent loop corrections to the higgs mass According to the documentary particle fever, the precise value of the higgs boson's mass could give more credence to either susy or multiverse theories
