Supersymmetric $\mathbb{CP}^1$ deformation and RG Flows

In the present paper we prove that the supersymmetric deformation of the $\mathbb{CP}^1$ sigma model – the supersymmetric generalization of the Fateev-Onofri-Zamolodchikov model, can be given in the form of the generalised Gross-Neveu model. It appears natural to exploit this field-theoretic formalism to compute one- and two-loop beta-function and establish that in the UV the theory flows to the super-Thirring model. We explicitly show that the last is equivalent to a sigma model with "cylinder" target space by computing correlators of primaries on both sides. Moreover, we also discover other conformal limits that emerge from our superdeformed construction. A discussion on further generalizations to Non-Kahler targets and relation to (mirror) integrable hierarchies is provided.