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<p>In this work, we investigate off-shell supersymmetric string configurations in Euclidean Ad𝕊<sub>5</sub> <i>×</i> 𝕊<sup>5</sup> background. By extending the Green-Schwarz supersymmetric equations using the pure spinor formalism, we demonstrate that while the solutions to the Green-Schwarz equations are necessarily minimal surfaces, the solutions to the extended equations form infinite-dimensional families, even with fixed boundary conditions, thus preventing direct derivations of exact results via supersymmetric localization. For concreteness, we have selected a supercharge that localizes the off-shell supersymmetric configurations to an Ad𝕊<sub>4</sub> <i>×</i> 𝕊<sup>2</sup> slice and observed that the corresponding action functional reduces to an integral of a two-form.</p>

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Supersymmetric string configurations in Ad𝕊5 × 𝕊5

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  • 发表日期：

    2025年4月1日

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  • Lucas N. S. Martins

摘要

In this work, we investigate off-shell supersymmetric string configurations in Euclidean Ad𝕊5 × 𝕊5 background. By extending the Green-Schwarz supersymmetric equations using the pure spinor formalism, we demonstrate that while the solutions to the Green-Schwarz equations are necessarily minimal surfaces, the solutions to the extended equations form infinite-dimensional families, even with fixed boundary conditions, thus preventing direct derivations of exact results via supersymmetric localization. For concreteness, we have selected a supercharge that localizes the off-shell supersymmetric configurations to an Ad𝕊4 × 𝕊2 slice and observed that the corresponding action functional reduces to an integral of a two-form.