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<p>We discuss two physics-inspired approaches to derivation of the eigenfunctions and eigenvalues of <i>A</i><sub><i>N</i></sub> Ruijsenaars-Schneider model. First approach which was recently proposed by the authors relies on the computations of superconformal indices of class <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25451_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">S</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{S} \)</EquationSource> </InlineEquation> 4<i>d</i> <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25451_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 2 theories with the insertion of surface defects. Second approach uses computations of Nekrasov-Shatashvili limit of 5<i>d</i> <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25451_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1<sup>*</sup> instanton partition functions in the presence of co-dimension two defect. We compare results of these two approaches for the low-lying levels of Ruijsenaars-Schneider model. We also discuss different previously proposed exact quantization conditions for the Coulomb branch parameters of the instanton partition functions and their interpretations in terms of index calculations.</p>

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On Ruijsenaars-Schneider spectrum from superconformal indices and ramified instantons

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  • 发表日期：

    2025年2月4日

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  • Hee-Cheol Kim,
  • Anton Nedelin,
  • Shlomo S. Razamat

摘要

We discuss two physics-inspired approaches to derivation of the eigenfunctions and eigenvalues of AN Ruijsenaars-Schneider model. First approach which was recently proposed by the authors relies on the computations of superconformal indices of class S \( \mathcal{S} \) 4d N \( \mathcal{N} \) = 2 theories with the insertion of surface defects. Second approach uses computations of Nekrasov-Shatashvili limit of 5d N \( \mathcal{N} \) = 1* instanton partition functions in the presence of co-dimension two defect. We compare results of these two approaches for the low-lying levels of Ruijsenaars-Schneider model. We also discuss different previously proposed exact quantization conditions for the Coulomb branch parameters of the instanton partition functions and their interpretations in terms of index calculations.