We investigate some properties of the standard rotator approximation of the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime. In particular we show that the isospin susceptibility calculated in this framework agrees with that computed by chiral perturbation theory up to next-to-next to leading order in the limit $\ell=L_t/L\to\infty\,.$ The difference between the results involves terms vanishing like $1/\ell\,,$ plus terms vanishing exponentially with $\ell\,$. As we have previously shown for the O($n$) model, this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in 2 dimensions for $N=3\,.$

中文翻译：

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关于 Delta 状态下 SU (N) × SU (N) sigma 模型的旋转子哈密顿量

我们研究了 SU$(N)\times\,$SU$(N)$ sigma-model 在 delta-regime 的标准旋转器近似的一些属性。特别是我们表明，在此框架中计算的同位旋磁化率与通过手性微扰理论计算的结果一致，直到在极限 $\ell=L_t/L\to\infty\,.$ 的差异结果之间涉及像 $1/\ell\,,$ 这样消失的项，加上以 $\ell\,$ 呈指数消失的项。正如我们之前为 O($n$) 模型展示的那样，这种偏差可以通过对与二次 Casimir 不变量的平方成正比的旋转器谱的校正来描述。在这里，我们在 $N=3\,.$ 的二维频谱上用解析非微扰结果来面对这个期望