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Abstract <p>We suggest supersymmetric generalization of the Ruijsenaars wave functions, write for them the corresponding difference equation and explain how they appear as one-point S matrix of modular transformation in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N = 1\)</EquationSource> <!--PhysPNLt2570169Apresyan-m1--> </InlineEquation> supersymmetric Liouville field theory. We also comment on their relation with the partition function of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(T[SU(2)]\)</EquationSource> <!--PhysPNLt2570169Apresyan-m2--> </InlineEquation> three-dimensional <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(N = 2\)</EquationSource> <!--PhysPNLt2570169Apresyan-m3--> </InlineEquation> supersymmetric gauge theory on squashed three-sphere modded by <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({{\mathbb{Z}}_{2}}\)</EquationSource> <!--PhysPNLt2570169Apresyan-m4--> </InlineEquation> action.</p>

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On Many Faces of Ruijsenaars Wave Functions

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • E. Apresyan,
  • Gor Sarkissian

摘要

Abstract

We suggest supersymmetric generalization of the Ruijsenaars wave functions, write for them the corresponding difference equation and explain how they appear as one-point S matrix of modular transformation in \(N = 1\) supersymmetric Liouville field theory. We also comment on their relation with the partition function of \(T[SU(2)]\) three-dimensional \(N = 2\) supersymmetric gauge theory on squashed three-sphere modded by \({{\mathbb{Z}}_{2}}\) action.