Supersymmetric σ-models on toric varieties: a test case

In this work we study supersymmetric σ-models on toric varieties. These manifolds are generalizations of Pⁿ manifolds. We examine here σ-models, viewed as gauged linear σ-models, on one of the simplest such manifold, the blow-up of P_(2,1,1)², and determine their properties using the techniques of topological-antitopological fusion. We find that the model contains solitons which become massless at the singular point of the theory where a gauge symmetry remains unbroken.