Sphalerons, Merons and Unstable Branes in AdS

TL;DR

This paper constructs and analyzes unstable solutions in Yang-Mills theories and their duals in AdS space, providing a non-supersymmetric test of the AdS/CFT correspondence through sphalerons, merons, and unstable branes.

Contribution

It introduces explicit unstable classical solutions in Yang-Mills theories and their dual unstable states in AdS, linking sphalerons, merons, and unstable branes in a non-supersymmetric context.

Findings

Unstable D0-branes in AdS correspond to sphalerons in the dual gauge theory.

D0-branes are dual to gauge theory merons with half-instanton charge.

The work supports Sen's hypothesis on unstable branes via weakly coupled dual field theory.

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.