On D= 2 (1/3,1/3) supersymmetric theories. I

Abstract

Using the D=2 (1/k,1/k) superalgebra (i.e. the two-dimensional generalized supersymmetry generated by spin s=1/k and -1/k; , charge operators Q and satisfying among other conditions and where P and are the light components of the energy--momentum operator), we build a superspace representation of this exotic symmetry. This realization generalizing the usual D=2 (1/2,1/2) supersymmetric one is based on the use of parafermionic variables and of spin s=-1/k and 1/k obeying as well as generalized commutation relation rules. Two-dimensional (1/3,0) and (1/3,1/3) invariant scalar superfield models extending the well-known D=2 (1/2,0) and (1/2,1/2) supersymmetric models are given. The link between this exotic symmetry and the periodic representation of with is worked out. Other features are also discussed.

Mechanical properties of natural rubber filled with flyash

“…This approach is different from the one in Refs. 32, 35, where nilpotent and cyclic representations of U q ( sl 2 ), with q 2 being a root of unity, are separately considered for an investigation of 𝒩 = 2 FSSQM in D = 1 + 1 dimensions. Second, the algebra U q ( sl 2 ) has not to be confused with the algebra spanned by the supercharges Q − and Q + and the Hamiltonian H .…”

“…The connection between FSSQM (and thus SSQM) and quantum groups has been worked out by several authors 32–40, mainly with applications to exotic statistics in mind. In particular, LeClair and Vafa 32 studied the isomorphism between the affine quantum algebra U q ( sl 2 ) and 𝒩 = 2 FSSQM in D = 1 + 1 dimensions when q 2 goes to a root of unity (𝒩 is the number of supercharges); in the special case where q 2 → −1, they recovered ordinary SSQM.…”

GELFAND–DICKEY ALGEBRA AND HIGHER SPIN SYMMETRIES ON T2 = S1 × S1

“…A particular choice of this arbitrary function leading to eqs. (19) and (22) is given by H(z, ω) = z −n 0 ω −m 0 .…”

Two approaches to fractional supersymmetrical quantum mechanics

“…This approach is different from the one in Refs. [32,35], where nilpotent and cyclic representations of U q (sl 2 ), with q 2 being a root of unity, are separately considered for an investigation of ᏺ ϭ 2 FSSQM in D ϭ 1 ϩ 1 dimensions. Second, the algebra U q (sl 2 ) has not to be confused with the algebra spanned by the supercharges Q Ϫ and Q ϩ and the Hamiltonian H. The latter algebra coincides with the Z 2 -graded Lie algebra sl(1/1) for q ϭ Ϫ1, i.e., k ϭ 2, in the case of ᏺ ϭ 2 SSQM.…”