Branes, Waves and AdS Orbifolds

TL;DR

Behrndt and Lüst analyze AdS orbifolds formed by pp-wave embeddings in brane worldvolumes and compare them to spherical orbifolds from Taub-NUT embeddings. They establish a U-duality between AdS orbifolds and spherical orbifolds and show that AdS orbifolds generically induce running couplings in the dual gauge theories, with the IR value $e^{2φ_{IR}}$ scaling as $N/k$ (opposite to the spherical case $k/N$). The paper provides explicit treatments of $AdS_3$ (BTZ) and extends to $AdS_5$, including single and double orbifolds and the associated pp-wave dynamics, elucidating how symmetry breaking and dilaton running arise from the global orbifold structure. Overall, it clarifies the duality between different geometric realizations of orbifolds and their implications for holography, running couplings, and localized brane intersections.

Abstract

The embedding of a Taub-NUT space in the directions transverse to the world volume of branes describes branes at (spherical) orbifold singularities. Similarly, the embedding of a pp-wave in the brane world volume yields an AdS orbifold. In case of the D1-D5--brane system, the AdS3 orbifolds yields a BTZ black hole; as we will show, the same holds for D3-branes corresponding to AdS5. In addition we will show that the AdS orbifolds and the spherical orbifolds are U-dual to each other. However in contrast to spherical orbifolds the AdS orbifolds lead to a running coupling, which is in the IR inverse to the coupling of the spherical orbifold. A discussion of the general pp-wave solution in AdS space is added.