Holographic Kondo model in various dimensions

Abstract

We study the addition of localised impurities to U(N) Supersymmetric Yang-Mills theories in (p + 1)-dimensions by using the gauge/gravity correspondence. From the gravity side, the impurities are introduced by considering probe D(8 − p)-branes extending along the time and radial directions and wrapping an (7 − p)-dimensional submanifold of the internal (8 − p)-sphere, so that the degrees of freedom are point-like from the gauge theory perspective. We analyse both the configuration in which the branes generate straight flux tubes — corresponding to actual single impurities — and the one in which connected flux tubes are created — corresponding to dimers. We discuss the thermodynamics of both the configurations and the related phase transition. In particular, the specific heat of the straight flux-tube configuration is negative for p < 3, while it is never the case for the connected one. We study the stability of the system by looking at the impurity fluctuations. Finally, we characterise the theory by computing one- and two-point correlators of the gauge theory operators dual to the impurity fluctuations. Because of the underlying generalised conformal structure, such correlators can be expressed in terms of an effective coupling constant (which runs because of its dimensionality) and a generalised conformal dimension.