Superdeformed $\mathbb{CP}$ $\sigma$-model equivalence

TL;DR

This paper introduces a new supersymmetric deformation of the $ ext{CP}^1$ sigma-model, demonstrating its equivalence to a generalized chiral Gross-Neveu model, and explores its implications for conformal limits and relations between different theoretical descriptions.

Contribution

It presents a novel supersymmetric deformation of the $ ext{CP}^1$ sigma-model and establishes its equivalence with the generalized chiral Gross-Neveu model, enabling new analytical approaches.

Findings

Established the equivalence between the deformed sigma-model and the chiral Gross-Neveu model.

Analyzed the renormalizability and $eta$-function of the deformed models.

Discussed the emergence of these models in $ ext{N}=2$ Liouville and 4D Chern-Simons theories.

Abstract

We find the novel class of the supersymmetric deformation of the $\mathbb{CP}^{1}$ $\sigma$-model and its equivalence with the generalised chiral Gross-Neveu. This construction allows the use of field-theoretic techniques and particularly the study of renormalisability and $\beta$-function. Provided approach is useful in finding conformal limits and establishes relation between chiral (GN) and sigma model description (geometric), which is explicitly demonstrated for the case of $ \mathbb{R} \times S^{1} $/Super-Thirring models. We also provide discussion on its emergence in $\mathcal{N}=2$ Liouville and 4-dim Chern-Simons theory.