On the Spectrum of Superspheres

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 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.