AdS Superalgebras with Brane Charges

TL;DR

The paper develops the inclusion of brane charges into AdS_5 superalgebras by identifying the maximal central extension of the boundary super-Poincaré algebra with the AdS_5 extension $OSp(1/8N,R)$, realized inside $Sp(8N,R)$ with the conformal group embedded as $SU(2,2) imes U(N)$. It maps out the 5-grading structure and the decomposition of spinor charges, showing how brane charges yield a consistent extension of the AdS_5 superalgebra and its boundary interpretation, while also exploring an intermediate extension $U(2N,2N/1)$. The authors extend the analysis to $AdS_7$ and $AdS_4$, and perform a detailed BPS-state analysis, uncovering R-symmetry breaking patterns tied to various brane configurations such as strings and membranes. They discuss the uniqueness and possible further symplectic extensions of these algebras, addressing implications for AdS/CFT, Coleman–Mandula constraints, and higher-dimensional unifications, including potential AdS_11/M-theory contexts.

Abstract

We consider the inclusion of brane charges in AdS_5 superalgebras that contain the maximal central extension of the super-Poincaré algebra on the boundary of AdS_5. For theories with N supersymmetries on the boundary, the maximal extension is OSp(1/8N,R), which contains the group $Sp(8N,R)\supset U(2N,2N) \supset SU(2,2)\times U(N)$ as extension of the conformal group. An ``intermediate'' extension to U(2N,2N/1) is also discussed, as well as the inclusion of brane charges in AdS_7 and AdS_4 superalgebras. BPS conditions in the presence of brane charges are studied in some details.