N=4 Sugawara Construction on <math> sl(2|1), sl(3)</math> and mKdV-type Superhierarchies

Physics NotePublished

N=4 Sugawara Construction on $<math> \widehat{sl(2|1)}, \widehat{sl(3)}</math>$ and mKdV-type Superhierarchies

E. Ivanov; S. Krivonos; F. Toppan

1999

Authors: E. Ivanov; S. Krivonos; F. Toppan
Type: Physics Note
Status: Published
Publication date: 1999
Description: The local Sugawara constructions of the "small" <math>N=4\,\!</math> SCA in terms of supercurrents of <math>N=2\,\!</math> extensions of the affine <math>\widehat{sl(2|1)}\,\!</math> and <math>\widehat{sl(3)}\,\!</math> algebras are investigated. The associated super mKdV type hierarchies induced by <math>N=4\,\!</math> SKdV ones are defined. In the <math>\widehat{sl(3)}\,\!</math> case the existence ofb two inequivalent Sugawara constructions is found. The "long" one involves all the affine <math>\widehat{sl(3)}\,\!</math> currents, while the "short" one deals only with those from the subalgebra <math>\widehat{sl(2)\oplus u(1)}\,\!</math> . As a consequence, the <math>\widehat{sl(3)}\,\!</math> -valued affine superfields carry two inequivalent mKdV type super hierarchies induced by the correspondence between "small" <math>N=4\,\!</math> SCA and <math>N=4\,\!</math> SKdV hierarchy. However, only the first hierarchy posseses genuine global <math>N=4\,\!</math> supersymmetry. We discuss peculiarities of the realization of this <math>N=4\,\!</math> supersymmetry on the affine supercurrents.
Year: 1999
Number: CBPF-NF-046/99
Linked to a thesis: No
Linked to a grant: No