$PSL(n|n)$ Sigma Model as a Conformal Field Theory

Details $PSL(n|n)$ Sigma Model as a Conformal Field Theory $PSL(n|n)$ Sigma Model as a Conformal Field Theory

1999-02-24

arxiv.org/abs/hep-th/9902180v2

Nucl.Phys.B559:205-234,1999

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, 5 figures

Scientific paper

10.1016/S0550-3213(99)00378-8

We discuss the sigma model on the $PSL(n|n)$ supergroup manifold. We demonstrate that this theory is exactly conformal. The chiral algebra of this model is given by some extension of the Virasoro algebra, similar to the $W$ algebra of Zamolodchikov. We also show that all group invariant correlation functions are coupling constant independent and can be computed in the free theory. The non invariant correlation functions are highly nontrivial and coupling dependent. At the end we compare two and three-point correlation functions of the $PSL(1,1|2)$ sigma model with the correlation functions in the boundary theory of $AdS_3 \times S^3$ and find a qualitative agreement.

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