D3-D7 holographic dual of a perturbed 3D CFT
D3-D7 holographic dual of a perturbed 3D CFT
复制标题
扰动 3D CFT 的 D3-D7 全息对偶
DOI：
10.1103/physrevd.88.026006
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发表时间：
2012
影响因子：
5
通讯作者：
G. Semenoff
中科院分区：
文献类型：
--
作者：
Hamid Omid;G. Semenoff
一个适当取向的D3-D 7膜系统是相对论性费米子的全息对偶，它占据了嵌入在3+1维时空中的2+1维缺陷。在3+1维体中，费米子通过${\mathcal N}=4$杨-米尔斯理论的场相互作用。近年来，利用内流在N_7 <<N_3极限下稳定系统，得到了一系列与含费米子的共形场论对偶的解，我们利用全息技术研究了相关算符对其中一个共形场论的扰动。一般来说，共形场论对这种微扰的响应在低能量尺度下增长并变得非微扰。我们将发现，打开背景磁场B和费米子质量m的微扰会引起重整化群流，这种重整化群流可以在小m ^2/B的极限下进行微扰研究。我们显式地求解首序。我们发现，对于一个特定的值的内部通量，该系统表现出磁催化，自发破缺的手征对称性增强的磁场的存在下。在此过程中，我们导出了有限密度下费米子-反费米子等离子体的德拜屏蔽长度和磁场存在下费米子系统基态的抗磁矩的计算公式。
An appropriately oriented D3-D7-brane system is the holographic dual of relativistic Fermions occupying a 2+1-dimensional defect embedded in 3+1-dimensional spacetime. The Fermions interact via fields of ${\mathcal N}=4$ Yang-Mills theory in the 3+1-dimensional bulk. Recently, using internal flux to stabilize the system in the probe $N_7<<N_3$ limit, a number of solutions which are dual to conformal field theories with Fermion content have been found. We use holographic techniques to study perturbations of a particular one of the conformal field theories by relevant operators. Generally, the response of a conformal field theory to such a perturbation grows and becomes nonperturbative at low energy scales. We shall find that a perturbation which switches on a background magnetic field $B$ and Fermion mass $m$ induces a renormalization group flow that can be studied perturbatively in the limit of small $m^2/B$. We solve the leading order explicitly. We find that, for one particular value of internal flux, the system exhibits magnetic catalysis, the spontaneous breaking of chiral symmetry enhanced by the presence of the magnetic field. In the process, we derive formulae predicting the Debye screening length of the Fermion-antiFermion plasma at finite density and the diamagnetic moment of the ground state of the Fermion system in the presence of a magnetic field.