标题： 超形变$\mathbb{CP}$ $σ$ -模型等价性 显示英文标题

标题： Superdeformed $\mathbb{CP}$ $σ$-model equivalence

摘要： 我们发现了超对称变形的一个新类，即$\mathbb{CP}^{1}$ $\sigma$ -模型，并证明了它与广义手征 Gross-Neveu 模型的等价性。这一构造允许使用场论技术，特别是可重整性和$\beta$-函数的研究。所提出的方法有助于寻找共形极限，并建立了手征（GN）和 sigma 模型描述（几何）之间的关系，这一点在$ \mathbb{R} \times S^{1} $/Super-Thirring 模型的情况下得到了明确展示。我们还讨论了它在$\mathcal{N}=2$Liouville 理论和 4 维 Chern-Simons 理论中的出现。 显示英文摘要

摘要： 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.