Supersymmetric string configurations in Ad𝕊5 × 𝕊5

A bstract In this work, we investigate off-shell supersymmetric string configurations in Euclidean Ad𝕊 5 × 𝕊 5 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 4 × 𝕊 2 slice and observed that the corresponding action functional reduces to an integral of a two-form.