Spectra of Sigma Models on Semi-Symmetric Spaces

TL;DR

This paper computes the one-loop anomalous dimensions of sigma models on semi-symmetric spaces, revealing a new XXZ-like interaction in the dilation operator, which is crucial for understanding string theories on AdS backgrounds.

Contribution

It determines the full one-loop dilation operator for these models, including a novel XXZ-like interaction term, advancing the understanding of their quantum properties.

Findings

Eigenvalues of the dilation operator are computed for specific examples.

A new XXZ-like interaction term appears in the one-loop dilation operator.

The models can be made conformal with a fermionic Wess-Zumino term under certain conditions.

Abstract

Sigma models on semi-symmetric spaces provide the central building block for string theories on AdS backgrounds. Under certain conditions on the global supersymmetry group they can be made one-loop conformal by adding an appropriate fermionic Wess-Zumino term. We determine the full one-loop dilation operator of the theory. It involves an interesting new XXZ-like interaction term. Eigenvalues of our dilation operator, i.e. the one-loop anomalous dimensions, are computed for a few examples.