论文标题
新的可集成的coset Sigma型号
New integrable coset sigma models
论文作者
论文摘要
通过使用Aggine Gaudin模型的一般框架，我们构建了一类新的可集成Sigma模型。它们的定义是在某个对角线子组上的谎言组的直接产品的固定位置定义，它们依赖于$ 3N-2 $免费参数。对于$ n = 1 $，相应的模型与众所周知的对称空间Sigma模型一致。从汉密尔顿的配方开始，我们为$ n = 2 $ case的拉格朗日派生，并表明它在经典的$ \ mathcal {r} $ - 基于这些模型的集成性的基础上接受了非常简单的形式。我们猜测，拉格朗日的类似形式也适用于任意$ n $。将我们的一般结构指定为$ su（2）$和$ n = 2 $的情况，并消除了其中一个参数，我们找到了一种新的三参数集成模型，其中歧管$ t {1,1,1} $是其目标空间。我们进一步评论结果与文献中存在的结果的联系。
By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of $N$ copies of a Lie group over some diagonal subgroup and they depend on $3N-2$ free parameters. For $N=1$ the corresponding model coincides with the well-known symmetric space sigma model. Starting from the Hamiltonian formulation, we derive the Lagrangian for the $N=2$ case and show that it admits a remarkably simple form in terms of the classical $\mathcal{R}$-matrix underlying the integrability of these models. We conjecture that a similar form of the Lagrangian holds for arbitrary $N$. Specifying our general construction to the case of $SU(2)$ and $N=2$, and eliminating one of the parameters, we find a new three-parametric integrable model with the manifold $T^{1,1}$ as its target space. We further comment on the connection of our results with those existing in the literature.
