D-branes and nonlinear interactions in the AdS pure spinor string

A bstract We develop a coordinate-independent algebraic description of zero-field boundary conditions for the pure spinor string on AdS 5 × S 5 in the closed-string channel. The construction is organized by involutive automorphisms of 𝔭𝔰𝔲(2, 2|4) that exchange the odd sectors of the ℤ 4 grading. Their fixed subalgebras provide candidate half-BPS, Lorentzian D-brane geometries with vanishing background world-volume flux, consistent with the standard AdS 2 , AdS 3 × S 1 , AdS 4 × S 2 , and related embeddings. Together, the seven representatives realize the Lorentzian zero-flux D1, D3, D5, and D7 probe sectors considered here. We then construct a local ansatz for the matter and ghost boundary interactions and derive a system of consistency equations for the tangential superconnection, transverse embedding, and four ghost-gluing couplings. The resulting system is a set of Dirac-Born-Infeld-like equations of motion on the brane world-volume.