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<p>We use analytic (super-)conformal bootstrap methods to derive explicit expressions for the structure constants of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1 Liouville CFT in the ‘timelike’ regime of the superconformal central charge. The obtained expressions take the form of inverses of the appropriate spacelike counterparts, which we explain concretely by elucidating the analytic properties of the corresponding shift relations in the NS- and R-sectors for the normalization-independent bootstrap data on the sphere. In a particular normalization, the timelike structure constants are shown to agree with the OPE coefficients of <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1 Minimal Models when specified at degenerate values of the momenta, exactly as in the non-supersymmetric case. We discuss possible applications of our results, with emphasis on the construction of the <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1 supersymmetric analog of the Virasoro Minimal String.</p>

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On the three-point functions in timelike \( \mathcal{N} \) = 1 Liouville CFT

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月23日

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  • Beatrix Mühlmann,
  • Vladimir Narovlansky,
  • Ioannis Tsiares

摘要

We use analytic (super-)conformal bootstrap methods to derive explicit expressions for the structure constants of N \( \mathcal{N} \) = 1 Liouville CFT in the ‘timelike’ regime of the superconformal central charge. The obtained expressions take the form of inverses of the appropriate spacelike counterparts, which we explain concretely by elucidating the analytic properties of the corresponding shift relations in the NS- and R-sectors for the normalization-independent bootstrap data on the sphere. In a particular normalization, the timelike structure constants are shown to agree with the OPE coefficients of N \( \mathcal{N} \) = 1 Minimal Models when specified at degenerate values of the momenta, exactly as in the non-supersymmetric case. We discuss possible applications of our results, with emphasis on the construction of the N \( \mathcal{N} \) = 1 supersymmetric analog of the Virasoro Minimal String.