Higher derivative supersymmetric nonlinear sigma models on hermitian symmetric spaces, and BPS states therein

We formulate four-dimensional N = 1 supersymmetric nonlinear sigma models on Hermitian symmetric spaces with higher derivative terms, free from the auxiliary field problem and the Ostrogradski’s ghosts, as gauged linear sigma models. We then study Bogomol’nyi-Prasad-Sommerfield equations preserving 1/2 or 1/4 supersymmetries. We find that there are distinct branches, that we call canonical (F = 0) and non-canonical (F 6= 0) branches, associated with solutions to auxiliary fields F in chiral multiplets. For the CP^N model, we obtain a supersymmetric CP^N Skyrme-Faddeev model in the canonical branch while in the non-canonical branch the Lagrangian consists of solely the CP^N Skyrme-Faddeev term without a canonical kinetic term. These structures can be extended to the Grassmann manifold G_M,N = SU(M)/[SU(M −N)×SU(N)×U(1)]. For other Hermitian symmetric spaces such as the quadric surface Q^N−2 = SO(N)/[SO(N − 2)×U(1)]), we impose F-term (holomorphic) constraints for embedding them into CP^N−1 or Grassmann manifold. We find that these constraints are consistent in the canonical branch but yield additional constraints on the dynamical fields thus reducing the target spaces in the non-canonical branch.