Title: A gauge invariant formulation for the SU(N) non-linear sigma model in 2+1 dimensions Show Chinese title

Title: 2+1维SU(N)非线性sigma模型的规范不变形式化

Abstract: We derive a local, gauge invariant action for the SU(N) non-linear sigma-model in 2+1 dimensions. In this setting, the model is defined in terms of a self-interacting pseudo vector-field \theta_\mu, with values in the Lie algebra of the group SU(N). Thanks to a non-trivially realized gauge invariance, the model has the correct number of degrees of freedom: only one polarization of \theta_\mu, like in the case of the familiar Yang-Mills theory in 2+1 dimensions. Moreover, since \theta_\mu is a pseudo-vector, the physical content corresponds to one massless pseudo-scalar field in the Lie algebra of SU(N), as in the standard representation of the model. We show that the dynamics of the physical polarization corresponds to that of the SU(N) non-linear sigma model in the standard representation, and also construct the corresponding BRST invariant gauge-fixed action. Show Chinese abstract

Abstract: 我们推导出一个局部的、规范不变的作用量，用于2+1维的SU(N)非线性sigma模型。 在这个设定下，该模型通过自相互作用的伪矢量场\theta _\mu 定义，其值位于SU(N)群的李代数中。 由于非平凡实现的规范不变性，该模型具有正确的自由度数目：仅\theta _\mu 的一种极化，类似于2+1维熟悉的杨-米尔斯理论的情况。 此外，由于\theta _\mu 是伪矢量，其物理内容对应于李代数中SU(N)的一个无质量伪标量场，如同模型的标准表示。 我们证明了物理极化的动力学与标准表示中的SU(N)非线性sigma模型的动力学相对应，并且还构造了相应的BRST不变规范固定的行动。