A Maximally Supersymmetric Kondo Model

Harrison, Sarah ; Kachru, Shamit ; Torroba, Gonzalo ; /Stanford U., Phys. Dept. /SLAC

SLAC National Accelerator Laboratory

关键词: Wilson Loop;    Fermi Gas;    Geometry;    Supergravity;    Yang-Mills Theory Theory-Hep,Hepth;   

DOI  :  10.2172/1035093
RP-ID  :  SLAC-PUB-14648
RP-ID  :  AC02-76SF00515
RP-ID  :  1035093

美国|英语

来源: UNT Digital Library

【 摘 要 】

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 S3 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.