Principal Chiral Model on Superspheres

TL;DR

This paper analyzes the spectrum of the principal chiral model on superspheres, providing evidence for a duality with Gross-Neveu models and computing boundary spectra for specific cases.

Contribution

It offers the first exact boundary spectrum calculations for supersphere PCMs and supports a conjectured duality with Gross-Neveu models.

Findings

Exact boundary spectrum for S^{3|2} computed as a function of R

Strong-weak coupling duality between supersphere PCMs and OSP(2S+2|2S) Gross-Neveu models supported

Discussion on extension to higher-dimensional superspheres

Abstract

We investigate the spectrum of the principal chiral model (PCM) on odd-dimensional superspheres as a function of the curvature radius R. For volume-filling branes on S^{3|2}, we compute the exact boundary spectrum as a function of R. The extension to higher dimensional superspheres is discussed, but not carried out in detail. Our results provide very convincing evidence in favor of the strong-weak coupling duality between supersphere PCMs and OSP(2S+2|2S) Gross-Neveu models that was recently conjectured by Candu and Saleur in arXiv:0801.0444.