All WZW Mooels in $D\leq5$
Abstract
We present here all the real algebras $\cal{A}$ with dim$\cal{A}\leq $5 and all 6dimensional nilpotent ones with symmetric, invariant and nondegenerate metrics for which a WZW model can be constructed. In three and four dimensions there are no other algebras than the well known $SU(2)$, $SU(1,1)$, $E_2^c$ and $H_4$. There exist only one fivedimensional and one sixdimensional nilpotent algebra with invariant nondegenerate metric and central charge $c=5, \,6$, respectively. We examine in details the fivedimensional case and, by gauging an appropriate subgroup, fourdimensional planewave string backgrounds are obtained. The corresponding background for the sixdimensional case is flat.
 Publication:

arXiv eprints
 Pub Date:
 June 1994
 arXiv:
 arXiv:hepth/9406136
 Bibcode:
 1994hep.th....6136K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 (kehagias@sci.kun.nl), 19 pages, LaTex, NTUA45/94