Review on Top-Down Kondo-like Holographic RG Flows

The Kondo model, i.e. the screening of magnetic impurities in a metal, has been a pillar of theoretical physics ever since its first establishment in 1964. This article provides an introduction to a recent top-down realization of the Kondo effect within the framework of the AdS/CFT correspondence, which appeared in [1,2]. These sources describe an entire class of Kondo-like renormalization group flows, based on $(p,q)$-string impurities embedded into $ads_3timesSS^3times M_4$, which all mimick the brane condensation description of the Kondo effect. In order to provide a lucid introduction, this review only discusses the simplest case of pure D1-brane impurities inside the F1/NS5 brane system. Choosing a stack of D1-branes occupying an $ads_2$ sheet within $ads_3$ and localized to a point on the $SS^3$ as UV configuration, the flow has the D1-branes puff up into D3-branes wrapping stably an $SS^2$ in the IR, whose polar angle on $SS^3$ is determined by the D1-brane charge of the system. This setup allows to describe the case where the impurity is exactly screened, just as in the original Kondo effect. Moreover, the $sfg$-factors are computed and shown to decrease along the flow, thereby confirming the validity of the $sfg$-theorem for this class of flows. This holographic model of the Kondo effect has two virtues. First, its ambient CFT is not only known, but also well studied. Second, the flow preserves the maximal amount of supersymmetry, i.e. four supercharges; these are enhanced to eight superconformal charges at the fixed points.