Hybrid classical integrability in squashed sigma models
Hybrid classical integrability in squashed sigma models
复制标题
压缩西格玛模型中的混合经典可积性
DOI：
10.1016/j.physletb.2011.09.117
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Kentaroh Yoshida
中科院分区：
文献类型：
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作者：
Io Kawaguchi;Kentaroh Yoshida
我们证明了SU（2）LYangian和q-变形SU（2）R对称性在三维压缩球上的二维sigma模型中得以实现。这些对称性使我们能够发展两种描述来描述它的经典动力学，1）有理描述和2）三角描述。前者1）基于SU（2）L对称性，后者2）来自SU（2）R对称性破缺。以两种方式构造的每个Lax对都导致相同的运动方程。这两个描述通过非本地映射相互关联。
We show that SU(2)LYangian and q-deformed SU(2)Rsymmetries are realized in a two-dimensional sigma model defined on a three-dimensional squashed sphere. These symmetries enable us to develop the two descriptions to describe its classical dynamics, 1) rational and 2) trigonometric descriptions. The former 1) is based on the SU(2)Lsymmetry and the latter 2) comes from the broken SU(2)Rsymmetry. Each of the Lax pairs constructed in both ways leads to the same equations of motion. The two descriptions are related to one another through a non-local map.