Scholarlink

<p>This paper is devoted to the quantum integrable structure of Wess-Zumino-Novikov-Witten models, formed by an infinite number of commuting Integrals of Motion (IMs) in their current algebra. Focusing for simplicity on the SU(2) case, we obtain the first four commuting higher-spin local IMs, starting from a general SU(2)-invariant ansatz and imposing their commutativity. We further show evidence of their commutativity with quantum non-local IMs, which were already built in the literature as Kondo defects. We then investigate the diagonalization of these local operators on <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mover accent="true"> <mrow> <mi mathvariant="fraktur">su</mi> <mfenced close=")" open="("> <mn>2</mn> </mfenced> </mrow> <mo stretchy="true">̂</mo> </mover> <mi>k</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {\hat{\mathfrak{su}(2)}}_k \)</EquationSource> </InlineEquation> Verma modules: we explicitly find the first few eigenvectors and further discuss the affine Bethe ansatz and ODE/IQFT conjectures, which predict the full eigenstates and spectrum of the integrable structure. Our results show a perfect match between the direct diagonalization and these overarching conjectures. We conclude by discussing several outlooks, including multi-current generalisations, massive deformations and a general long-term program towards the first principle quantisation of 2-dimensional integrable sigma-models.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the integrable structure of the SU(2) Wess-Zumino-Novikov-Witten model

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月16日

查看全文
  • Sylvain Lacroix,
  • Adrien Molines

摘要

This paper is devoted to the quantum integrable structure of Wess-Zumino-Novikov-Witten models, formed by an infinite number of commuting Integrals of Motion (IMs) in their current algebra. Focusing for simplicity on the SU(2) case, we obtain the first four commuting higher-spin local IMs, starting from a general SU(2)-invariant ansatz and imposing their commutativity. We further show evidence of their commutativity with quantum non-local IMs, which were already built in the literature as Kondo defects. We then investigate the diagonalization of these local operators on su 2 ̂ k \( {\hat{\mathfrak{su}(2)}}_k \) Verma modules: we explicitly find the first few eigenvectors and further discuss the affine Bethe ansatz and ODE/IQFT conjectures, which predict the full eigenstates and spectrum of the integrable structure. Our results show a perfect match between the direct diagonalization and these overarching conjectures. We conclude by discussing several outlooks, including multi-current generalisations, massive deformations and a general long-term program towards the first principle quantisation of 2-dimensional integrable sigma-models.