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<p>The study of three dimensional CFT correlators in twistor space has recently garnered a significant interest. Conformal symmetry acts linearly in the twistor space, which streamlines the analysis. Moreover, twistors provide a connection to the position and momentum space through the Penrose and Witten transforms, respectively. In this work, we develop the supersymmetric versions of Penrose and Witten transforms for three dimensional superconformal field theories for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{N}=1\)</EquationSource> </InlineEquation> to 4. We derive two and three point functions in the position and momentum superspace for the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{N}=1\)</EquationSource> </InlineEquation> scenario using these transforms. Extending this setup to higher supersymmetries turns out to be a simple extension of the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal{N}=1\)</EquationSource> </InlineEquation> case, which aligns with the inherent simplicity of supertwistors.</p>

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Super-Penrose & Witten transforms for SCFT3

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月4日

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  • Deep Mazumdar

摘要

The study of three dimensional CFT correlators in twistor space has recently garnered a significant interest. Conformal symmetry acts linearly in the twistor space, which streamlines the analysis. Moreover, twistors provide a connection to the position and momentum space through the Penrose and Witten transforms, respectively. In this work, we develop the supersymmetric versions of Penrose and Witten transforms for three dimensional superconformal field theories for \(\mathcal{N}=1\) to 4. We derive two and three point functions in the position and momentum superspace for the \(\mathcal{N}=1\) scenario using these transforms. Extending this setup to higher supersymmetries turns out to be a simple extension of the \(\mathcal{N}=1\) case, which aligns with the inherent simplicity of supertwistors.