A maximally supersymmetric Kondo model

TL;DR

This paper introduces a supersymmetric Kondo model within N=4 SYM, analyzing its holographic dual, stability, and thermodynamics, revealing new features due to the interacting conformal field theory environment.

Contribution

It establishes a holographic correspondence between the supersymmetric Kondo model and Wilson loops, and explores the geometric transition replacing D5-branes with flux in the gravity dual.

Findings

Holographic dictionary between Kondo impurity and Wilson loops

Explicit spectrum of defect operators and stability analysis

Description of the Kondo model via a geometric transition in supergravity

Abstract

We study the maximally supersymmetric Kondo model obtained by adding a fermionic impurity to N=4 supersymmetric Yang-Mills theory. While the original Kondo problem describes a defect interacting with a free Fermi liquid of itinerant electrons, here the ambient theory is an interacting CFT, and this introduces qualitatively new features into the system. The model arises in string theory by considering the intersection of a stack of M D5-branes with a stack of N D3-branes, at a point in the D3 worldvolume. We analyze the theory holographically, and propose a dictionary between the Kondo problem and antisymmetric Wilson loops in N=4 SYM. We perform an explicit calculation of the D5 fluctuations in the D3 geometry and determine the spectrum of defect operators. This establishes the stability of the Kondo fixed point together with its basic thermodynamic properties. Known supergravity solutions for Wilson loops allow us to go beyond the probe approximation: the D5s disappear and are replaced by three-form flux piercing a new topologically non-trivial three-sphere in the corrected geometry. This describes the Kondo model in terms of a geometric transition. A dual matrix model reflects the basic properties of the corrected gravity solution in its eigenvalue distribution.