Anti-de-Sitter D-branes

TL;DR

The work analyzes D-branes in the $SL(2,{f R})$ WZW model and its orbifolds, revealing a classification of two-dimensional world-volumes as twined conjugacy classes that include $H_2$, $dS_2$, and $AdS_2$ geometries. It shows $dS_2$ branes are unphysical due to a supercritical world-volume electric field, while $AdS_2$ branes arise as physically acceptable D-strings with tunable electric flux; combining these with $SU(2)$ branes yields supersymmetric $AdS_2 imes S^2$ D3-branes in the $AdS_3 imes S^3$ near-horizon background of NS5/F1 strings, with open-string effects enforcing equal world-volume radii and enabling noncommutative open-string regimes. The paper further analyzes the fate of these branes in BTZ black-hole geometries and discusses how supersymmetry can be preserved in related orbifold contexts via elliptic elements. Overall, it provides a semi-classical, CFT-consistent picture of D-branes in non-compact AdS backgrounds, highlighting open-string vs induced-geometries as a key feature of brane dynamics with potential implications for AdS/CFT and noncommutative field theories.

Abstract

We study D-branes of the ${SL(2,\bR)}$ WZW model, and of its discrete orbifolds. Gluing the currents by group automorphisms leads to three types of D-branes: two-dimensional hyperbolic planes ($H_2$), de Sitter branes (dS$_2$), or anti-de-Sitter branes (AdS$_2$). We explain that the dS$_2$ branes are unphysical, because the electric field on their worldvolume is supercritical. By combining ${SL(2,\bR)}$ and SU(2), we exhibit a class of supersymmetric AdS$_2\times S^2$ three-brane worldvolumes, and consider their possible embeddings in the near-horizon region of stringy black holes. We point out the intriguing difference between the induced and the effective geometries of these D-branes, and speculate on its possible significance.