A maximally supersymmetric Kondo model
A maximally supersymmetric Kondo model
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最大超对称近藤模型
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发表时间：
2011
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通讯作者：
G. Torroba
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作者：
Sarah M. Harrison;S. Kachru;G. Torroba
研究了在超对称Yang-Mills理论中加入费米子杂质后得到的极大超对称Kondo模型。虽然最初的近藤问题描述了一个缺陷与自由费米液体的巡回电子相互作用，在这里的环境理论是一个相互作用的CFT，这引入了定性的新功能的系统。这个模型在弦理论中通过考虑一堆M个D5-膜和一堆N个D3-膜在D3世界体积中的一个点上的相交而产生。我们全息分析的理论，并提出了一个字典之间的近藤问题和反对称威尔逊循环SYM。我们进行了显式计算的D3几何中的D5波动，并确定了缺陷运营商的频谱。这建立了Kondo不动点的稳定性以及它的基本热力学性质。威尔逊环的已知超引力解允许我们超越探测近似：D5消失，并被三种形式的通量取代，在修正的几何中穿透一个新的拓扑非平凡的S3。这描述了近藤模型的几何过渡。对偶矩阵模型在特征值分布上反映了重力修正解的基本性质。
We study the maximally supersymmetric Kondo model obtained by adding a fermionic impurity to 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 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.