After its invention, Supersymmetry is introduced into particle physics first as a global symmetry to solve hierarchy problem. However only after its promotion into a local gauge one and natural combination with gravity, more interesting and robust predictions can be made. On the other hand, when people investigate extra dimensional senarior or moduli compacitification to produce low energy effective theory close to our reality from some UV completed mother theory, for instance string theory or M-theory, if supersymmetry is preserved, the study can be much more simplified.
What we want to study in the previous year is the supersymmetric gravity background and gravity fluctuation on it. Then it turns out not only this problem is too complicated, but even the background coupling to general super multilplet is not well-studied. In particular, the most general hypermultiplets coupling to 5D anti-de Sitter space background is still an open question. So from July, we turn our focus mainly to this project and hope to find a solution.
5D anti-de Sitter has been well studied for its close relation to conformal quantum field theory in 4D. Its isometry group is identical to conformal group in 4D, its irreducible representation can be then derived. However the technique difficulty is still there: the fermion representation in 5D must take either Dirac 4-component type or symplectic Majorana type, while 4D fermion can take Majorana or Weyl 2-component type. So in this project, we choose all fermion notation to be unconstrinted 4 component Dirac type and decomposite it into 2 component Weyl type from time to time, which will help us to compare with other well-known N=2 result in 4D.