New supersymmetry algebra on gravitational interaction of Nambu–Goldstone fermion

The spacetime symmetries of SGM action proposed as the gravitational coupling of N–G fermions are investigated. The commutators of new nonlinear supersymmetry (NL SUSY) transformations form a closed algebra, which reveals N–G fermion (NL SUSY) nature and a generalized general coordinate transformation. A generalized local Lorentz transformation, which forms a closed algebra, is also introduced.