All WZW Mooels in $D\leq5$

Details All WZW Mooels in $D\leq5$ All WZW Mooels in $D\leq5$

1994-06-21

arxiv.org/abs/hep-th/9406136v1

Physics

High Energy Physics

High Energy Physics - Theory

(kehagias@sci.kun.nl), 19 pages, LaTex, NTUA-45/94

Scientific paper

We present here all the real algebras $\cal{A}$ with dim$\cal{A}\leq $5 and all 6-dimensional nilpotent ones with symmetric, invariant and non-degenerate 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 five-dimensional and one six-dimensional nilpotent algebra with invariant non-degenerate metric and central charge $c=5, \,6$, respectively. We examine in details the five-dimensional case and, by gauging an appropriate subgroup, four-dimensional plane-wave string backgrounds are obtained. The corresponding background for the six-dimensional case is flat.

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