强耦合BCS超导与全息
Strong Coupling BCS Superconductivity and Holography
摘要：
本文试图给出BCS超导体微观理论的全息描述。利用QCD中手征对称性破缺的类比，我们使用了在有限重子数的D4膜背景中的两个D8膜的Sakai-Sugimoto模型。在这种情况下，有一个新的快子不稳定性，这可能是库珀配对不稳定性的大块模拟。我们分析了非阿贝尔Born-Infeld作用的Yang-Mills近似。给出了平坦空间中非线性Yang-Mills方程的精确解，并进行了稳定性分析，指出当存在电场时，不稳定性消失.全息图还表明，$T_c$依赖于数密度，这是不同于通常的（弱耦合）BCS。平面空间的解决方案，然后推广到弯曲的空间数值，也以近似的方式，解析。然后，该配置应该对应于边界超导（超流体）基态的基态。我们还给出了在没有化学势的Sakai-Sugimoto模型中格林函数计算的一些初步结果
英文摘要：
We attempt to give a holographic description of the microscopic theory of a BCS superconductor. Exploiting the analogy with chiral symmetry breaking in QCD we use the Sakai-Sugimoto model of two D8 branes in a D4 brane background with finite baryon number. In this case there is a new tachyonic instability which is plausibly the bulk analog of the Cooper pairing instability. We analyze the Yang-Mills approximation to the non-Abelian Born-Infeld action. We give some exact solutions of the non-linear Yang-Mills equations in flat space and also give a stability analysis, showing that the instability disappears in the presence of an electric field. The holograhic picture also suggests a dependence of $T_c$ on the number density which is different from the usual (weak coupling) BCS. The flat space solutions are then generalized to curved space numerically and also, in an approximate way, analytically. This configuration should then correspond to the ground state of the boundary superconducting (superfluid) ground state. We also give some preliminary results on Green functions computations in the Sakai - Sugimoto model without any chemical potential
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