Sphalerons, Merons and Unstable Branes in AdS
Nadav Drukker, David J. Gross, N. Itzhaki
TL;DR
This work investigates non-BPS, unstable configurations in the AdS/CFT framework by identifying sphalerons in gauge theory on $S^3\times\mathbb{R}$ with unstable D0-branes at the center of $AdS_5\times S^5$, thereby providing a non-supersymmetric test of the duality. It extends the correspondence to Euclidean signatures by pairing gauge-theory merons with D0-branes in Euclidean $AdS$, showing that each end of a D0-brane carries half a D-instanton charge and that unstable branes can be viewed as D-merons. The paper then generalizes to unstable branes of higher dimensionality and to unstable strings in the Coulomb phase, where gauge theory solitons map to non-BPS brane/flux configurations in gravity, including half-monopole constructions in the dual supergravity background. Together, these results provide a coherent topological and dynamical picture linking non-BPS gauge configurations to D-brane saddles, supporting the AdS/CFT correspondence beyond supersymmetric sectors and offering a concrete realization of Sen’s unstable-brane ideas within a strongly coupled gauge/string duality.
Abstract
We construct unstable classical solutions of Yang-Mills theories and their dual unstable states of type IIB on AdS_5. An example is the unstable D0-brane of type IIB located at the center of AdS. This has a field theory dual which is a sphaleron in gauge theories on S^3 x R. We argue that the two are dual because both are sphalerons associated to the topology of the instanton/D-instanton. This agreement provides a non-supersymmetric test of the AdS/CFT duality. As an illustration, many aspects of Sen's hypothesis regarding the unstable branes can be seen easily in the weakly coupled dual field theory description. In Euclidean AdS the D0-branes are dual to gauge theory merons. This implies that the two ends of a D0-brane world-line carry half the charge of a D-instanton. Other examples involve unstable strings in the Coulomb phase.