Quantum affine symmetry as generalized supersymmetry

Abstract

The quantum affine U q( ( sl(2) ) symmetry is studied when q 2 is an even root of unity. The structure of this algebra allows a natural generalization of N = 2 supersymmetry algebra. In particular it is found that the momentum operators P, P , and thus the hamiltonian, can be written as generalized multi-commutators, and can be viewed as new central elements of the algebra U q( sl(2) ) . We show that massive particles in (deformationsof) integer spin representations of sl(2) are not allowed in such theories. Generalizations of Witten's index and Bogomolnyi bounds are presented and a preliminary attempt in constructing manifestly U q( ( sl(2) ) invariant actions as generalized supersymmetric Landau-Ginzburg theories is made.