Higher derivative supersymmetric nonlinear sigma models on Hermitian symmetric spaces and BPS states therein
Higher derivative supersymmetric nonlinear sigma models on Hermitian symmetric spaces and BPS states therein
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DOI：
10.1103/physrevd.103.025001
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发表时间：
2020-11
期刊：
影响因子：
--
通讯作者：
M. Nitta;S. Sasaki
中科院分区：
文献类型：
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作者：
M. Nitta;S. Sasaki
在具有高阶导数项的厄米特对称空间上，我们建立了四维数学{N}=1$超对称非线性sigma模型，该模型不受辅助场问题和Ostrogradski鬼魂的影响，是规范线性sigma模型.然后我们研究了保持1/2或1/4超对称的Bogomol‘nyi-Prasad-Sommerfield方程。我们发现有不同的分支，我们称之为正则分支($F=0$)和非正则分支($F\neq 0$)，它们与手征多重态中辅助场$F$的解有关。对于P^N$模型，我们在正则支中得到了超对称的P^N Skyrme-Faddeev模型，而在非正则支中，拉格朗日仅由P^N=Skyrme-Faddeev项组成，没有正则动力学项。这些结构可以推广到Grassmann流形$G_{M，N}=SU(M)/[SU(M-N)\×SU(N)\×U(1)]$。对于其他Hermite对称空间，例如二次曲面$Q^{N-2}=SO(N)/[SO(N-2)\x U(1)])$，我们施加F-项(全纯)约束以将它们嵌入到${mathbb C}P^{N-1}$或Grassmann流形中。我们发现，这些约束在正则分支中是一致的，但对动态场产生了额外的约束，从而减少了非正则分支中的靶空间。
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.