Helical Luttinger liquids and three-dimensional black holes
Helical Luttinger liquids and three-dimensional black holes
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DOI：
10.1103/physrevd.84.126012
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发表时间：
2010-12
影响因子：
5
通讯作者：
V. Balasubramanian;Inaki Garc'ia-Etxebarria;F. Larsen;J. Sim'on
中科院分区：
文献类型：
--
作者：
V. Balasubramanian;Inaki Garc'ia-Etxebarria;F. Larsen;J. Sim'on
我们使用的AdS/CFT对应讨论之间的等价性螺旋，强耦合Luttinger液体和费米子传播的背景下的拓扑带电黑洞在三维空间。费米能级由拓扑荷决定，克服了库仑荷电黑洞标准方法在低维情况下的困难。这种构造完全可以嵌入弦理论，微观拉格朗日量也是明确已知的。在低温和低能量下的延迟绿色函数产生于非常接近黑洞视界的几何结构，这种结构对于所有冷的带电液体都是通用的，在引力中具有对偶$\mathbb{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}（1{）}^{s}$不变描述。这解释了Luttinger物理学和AdS/CFT对应中高维非费米液体的红外行为之间的微妙关系。
We use the AdS/CFT correspondence to discuss an equivalence between a helical, strongly coupled Luttinger liquid and a fermion propagating in the background of a topologically charged black hole in three dimensions. The Fermi level is set by the topological charges, thus surmounting difficulties in low dimensions of the standard approach using Coulomb charged black holes. The construction is fully embeddable in string theory, and the microscopic Lagrangian is explicitly known. The retarded Green function at low temperature and energy arises from the geometry very near the black hole horizon, a structure that is universal for all cold, charged liquids with a dual $\mathbb{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}^{s}$ invariant description in gravity. This explains a subtle relationship between Luttinger physics and the infrared behavior of higher dimensional non-Fermi liquids in the AdS/CFT correspondence.