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Abstract <p>We find the novel supersymmetric deformation of the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb{C}{{\mathbb{P}}^{1}}\)</EquationSource> <!--PhysPNLt2570167Pribytok-m3--> </InlineEquation> σ-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 β function. Provided approach is useful in finding conformal limits and establishes relation between chiral (GN) and sigma model (geometric) descriptions, which is explicitly demonstrated for the case of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb{R} \times {{S}^{1}}\)</EquationSource> <!--PhysPNLt2570167Pribytok-m4--> </InlineEquation>/Super-Thirring models. We also make remarks on its emergence in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal{N} = 2\)</EquationSource> <!--PhysPNLt2570167Pribytok-m5--> </InlineEquation> Liouville and 4-dim Chern–Simons theory.</p>

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Superdeformed \(\mathbb{C}\mathbb{P}\) σ-Model Equivalence

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • A. Pribytok

摘要

Abstract

We find the novel supersymmetric deformation of the \(\mathbb{C}{{\mathbb{P}}^{1}}\) σ-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 β function. Provided approach is useful in finding conformal limits and establishes relation between chiral (GN) and sigma model (geometric) descriptions, which is explicitly demonstrated for the case of \(\mathbb{R} \times {{S}^{1}}\) /Super-Thirring models. We also make remarks on its emergence in \(\mathcal{N} = 2\) Liouville and 4-dim Chern–Simons theory.