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arXiv · hep-th/9210009

Quantum Affine Symmetry as Generalized Supersymmetry

A. LeClair·C. Vafa
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Abstract

The quantum affine $\CU_q (\hat{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 $P ,\bar{P}$, and thus the Hamiltonian, can be written as generalized multi-commutators, and can be viewed as new central elements of the algebra $\CU_q (\hat{sl(2)})$. We show that massive particles in (deformations of) integer spin representions 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 $\CU_q (\hat{sl(2)})$ invariant actions as generalized supersymmetric Landau-Ginzburg theories is made.

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A. LeClair, C. Vafa. 1992-10-01. Quantum Affine Symmetry as Generalized Supersymmetry. https://doi.org/10.1016/0550-3213(93)90309-d

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