On the Spectrum of Superspheres
Alessandra Cagnazzo, Volker Schomerus, Vaclav Tlapak

TL;DR
This paper analyzes the spectrum of supersphere sigma models, constructs vertex operators, and explores a duality with the Gross-Neveu model, providing explicit anomalous dimensions and examining the spectrum correspondence.
Contribution
It applies recent spectrum results to supersphere sigma models, constructs vertex operators, and revisits a duality with the Gross-Neveu model with explicit calculations.
Findings
Explicit formulas for anomalous dimensions of vertex operators
Recovery of the zero mode spectrum at finite Gross-Neveu coupling
Discussion of potential high-gradient operator instabilities
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 1/2 BPS 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…
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