On the rotator Hamiltonian for the SU (N) × SU (N) sigma model in the delta regime

Abstract

Abstract We investigate some properties of the standard rotator approximation of the $\mathrm{SU}(N)\times\mathrm{SU}(N)$ 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 two dimensions for $N=3$.