Abstract
SU(2|1) supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an mathcal{N}=4 supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra widehat{su}left(2Big|1right) . The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum SU(2|1) generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.
Highlights
Calogero-Moser systems can provide a microscopic description of the extreme ReissnerNordstrom black hole in the near-horizon limit
Supersymmetric Calogero-Moser systems have further applications in string theory and N = 4 super Yang-Mills theory [11, 12]. Keeping in mind these physical and mathematical motivations, it seems of great interest to construct and study new versions of supersymmetric Calogero-type systems
In a recent paper [13], there was proposed the superfield matrix model of SU(2|1) supersymmetric mechanics1 as a new N = 4 extension of d = 1 Calogero-Moser multiparticle system. This matrix model is a massive generalization of the multiparticle N = 4 model constructed and studied in [24, 25]
Summary
The Hamiltonian (2.1) involves the matrix momentum Pab ≡ (∇X)ab and another matrix quantity. Due to the resolved form of gauge-fixing conditions, new Dirac brackets for the remaining variables coincide with (2.7):. Where Aa = Aaa (no summation over a) and the generalized Calogero-Moser Hamiltonian is defined as. One more matrix present in the action (2.24) is Tab defined in (2.16) These quantities form u(n) algebra (2.9) with respect to the Dirac brackets: Tab, Tcd δadTcb − δcbTad (2.32). The Hamiltonian (2.38) contains a potential in the center-of-mass sector with the coordinate X0 (the last term in (2.38)) Modulo this extra potential, the bosonic limit of the system constructed is none other than the U(2)-spin Calogero-Moser model which is a massive generalization of the U(2)-spin Calogero model [28, 29, 31,32,33]. The system (2.24) with the Hamiltonian (2.23) describes SU(2|1) supersymmetric extension of the U(2)-spin Calogero-Moser model
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