Exact spectrum and partition function of \(SU(m|n)\) supersymmetric Polychronakos model (Q2718297)

By using the fact that Polychronakos-like models can be obtained through the `freezing limit' of related spin Calogero models, we calculate the exact spectrum as well as the partition function of the \(SU(m|n)\) supersymmetric Polychronakos (SP) model. It turns out that, similar to the non-supersymmetric case, the spectrum of the \(SU(m|n)\) SP model is also equally spaced. However, the degeneracy factors of corresponding energy levels crucially depend on the values of bosonic degrees of freedom \((m)\) and fermionic degrees of freedom \((n)\). As a result, the partition functions of the SP models are expressed with some novel \(q\)-polynomials. Finally, by interchanging the bosonic and fermionic degrees of freedom, we obtain a duality relation among the partition functions of the SP models.