ON SUPERSYMMETRIC EXTENDED CONFORMAL ALGEBRAS AND SUPER KP HIERARCHY
- 10 October 1989
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics A
- Vol. 4 (16) , 4083-4095
- https://doi.org/10.1142/s0217751x89001680
Abstract
We consider a possible supersymmetric generalization of the extended conformal algebra with a Z3 symmetry. By drawing analogy from the connection of the KdV hierachy and the conformal algebra, which is a particular case of KP hierachy, we approach the problem in a superspace formalism of the super KP hierachy. A generalization of the Miura transformation and accompanying factorization of the Lax operator is examined. We conclude that the nontrivial factorization of the Lax operator is impossible and thus a nontrivial supersymmetric version of the extended conformal algebra cannot be constructed. We argue that the impossibility is due to the incompatibility of the Z2 grading and Z3 symmetry of the system.Keywords
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