N=4 supersymmetric Calogero-Sutherland models

Abstract

Starting from the Hamiltonian formulation of supersymmetric Calogero models associated with the classical An, Bn, Cn and Dn series we construct the N = 2 and N = 4 supersymmetric extensions of the their hyperbolic/trigonometric Calogero-Sutherland cousins. The bosonic core of these models are the standard Calogero-Sutherland hyperbolic/trigonometric systems.

N=2supersymmetric hyperbolic Calogero-Sutherland model

“…were introduced in [16]. In these quantities the supercharges (3.5), (3.6) take the form 18) where β = −1, and coincide exactly with the N = 4 supersymmetry generators presented in [19]. 1 Point out that in contrast to the properties of the Grassmannian variables (2.22), quantities (5.16) do not form pairs with respect to complex conjugation, that is some obstacle in quantization of the system in such representation.…”

“…As result, we get the N = 4 supersymmetric system with n first class constraints (5.9), which allows us gauging of the remaining spinning variables. Such a reduced system is in fact the N = 4 generalization of the spinless hyperbolic Calogero-Sutherland system equivalent to the model presented in [19].…”

“…The author thanks Sergey Krivonos for the information that the value β = −1 is also valid in the hyperbolic case of the model presented in[19].…”

“…One of the important developments in the study of the famous many-particle Calogero-Sutherland systems [1,2] (see [3,4] for reviews) is their generalization to supersymmetric cases. Most of the researches in these directions have been devoted to supersymmetrization of the rational Calogero systems (see, for example, the papers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the review [20]). Supersymmetric generalizations of the hyperbolic and trigonometric Calogero-Sutherland systems have been studied in a very limited number of works (see, for example, the papers [17][18][19][21][22][23][24][25][26][27] and references therein).…”

New $$ \mathcal{N} $$= 2 superspace Calogero models

“…In the series of papers [13][14][15] we developed a different approach. Mainly working in the Hamiltonian formulation, we worked out an ansatz for the supercharges which accommodates all Calogero models associated with the classical A n , B n , C n and D n Lie algebras and their trigonometric/hyperbolic extensions [15]. Having at hands the Hamiltonian description of N -extended supersymmetric Calogero models, it is of interest to gain also its superfield formulation, at least in the simplest case of N = 2 supersymmetry.…”