Abstract
Sigma models on coset superspaces, such as odd dimensional superspheres, play an important role in physics and in particular the AdS/CFT correspondence. In this work we apply recent general results on the spectrum of coset space models and on supergroup WZNW models to study the conformal sigma model with target space S 3|2. We construct its vertex operators and provide explicit formulas for their anomalous dimensions, at least to leading order in the sigma model coupling. The results are used to revisit a non-perturbative duality between the supersphere and the OSP(4|2) Gross-Neveu model that was conjectured by Candu and Saleur. With the help of powerful all-loop results for $$ \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} $$ operators in the Gross-Neveu model we are able to recover the entire zero mode spectrum of the sigma model at a certain finite value of the Gross-Neveu coupling. In addition, we argue that the sigma model constraints and equations of motion are implemented correctly in the dual Gross-Neveu description. On the other hand, high(er) gradient operators of the sigma model are not all accounted for. It is possible that this discrepancy is related to an instability from high gradient operators that has previously been observed in the context of Anderson localization.
Highlights
Sigma models on coset superspaces, such as odd dimensional superspheres, play an important role in physics and in particular the AdS/CFT correspondence
While we believe that most of the ideas we are going to develop below apply to a wide class of sigma models on such generalized symmetric superspaces, our presentation and analysis will focus on the coset superspace OSP(4|2)/OSP(3|2) for which the analysis can be made very explicit
In this work we have reviewed recent results on the spectrum of coset sigma models and applied them to the conformal supersphere sigma model with target space S3|2
Summary
The aim of this section is to review some results from [9] concerning the spectrum of sigma models on symmetric superspaces. After a bit of introduction we shall build a basis of fields in sigma models on coset (super-)spaces G/H. At least when G/H is symmetric our basis diagonalizes the one-loop dilation operator and we can give a very simple formula for the spectrum of one-loop anomalous dimensions. The material of this section has been. Split into three different subsections of decreasing generality. While the construction of field operators in the first subsection holds for all coset models G/H, our discussion of the zero modes is limited to compact G. Results on the one-loop spectrum have only been obtained for symmetric (super-)spaces, though an extension to generalized symmetric spaces is under investigation
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