Higher Derivative Supersymmetric Nonlinear Sigma Models on Hermitian Symmetric Spaces, and BPS States Therein

TL;DR

This paper develops higher derivative supersymmetric nonlinear sigma models on Hermitian symmetric spaces, explores BPS states, and reveals distinct solution branches with implications for models like ${f C}P^N$ and Grassmann manifolds.

Contribution

It formulates ghost-free higher derivative supersymmetric sigma models on Hermitian symmetric spaces and analyzes their BPS solutions, including novel canonical and non-canonical branches.

Findings

Constructed ghost-free higher derivative models on Hermitian symmetric spaces.

Identified distinct solution branches with different auxiliary field configurations.

Extended structures to Grassmann and quadric target spaces.

Abstract

We formulate four-dimensional $\mathcal{N} = 1$ 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 ($F\neq 0$) branches, associated with solutions to auxiliary fields $F$ in chiral multiplets. For the ${\mathbb C}P^N$ model, we obtain a supersymmetric ${\mathbb C}P^N$ Skyrme-Faddeev model in the canonical branch while in the non-canonical branch the Lagrangian consists of solely the ${\mathbb C}P^N$ Skyrme-Faddeev term without a canonical kinetic term. These structures can be extended to the Grassmann manifold $G_{M,N} = SU(M)/[SU(M-N)\times SU(N) \times U(1)]$. For other Hermitian symmetric spaces such as the quadric surface $Q^{N-2}=SO(N)/[SO(N-2) \times U(1)])$, we impose F-term (holomorphic) constraints for embedding them into ${\mathbb C}P^{N-1}$ 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.