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

TL;DR

This paper demonstrates that the $PSL(n|n)$ sigma model is exactly conformal, with a complex chiral algebra extension, and explores correlation functions, showing some are coupling independent and others are highly nontrivial, with applications to $AdS_3$ boundary theories.

Contribution

It establishes the exact conformality of the $PSL(n|n)$ sigma model and analyzes its chiral algebra and correlation functions, connecting to $AdS_3$ boundary theories.

Findings

The model is exactly conformal.

Group invariant correlators are coupling constant independent.

Non-invariant correlators are coupling dependent and complex.

Abstract

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.