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arXiv 1902.04279hep-thhep-lathep-ph
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全息RG流中的有效长距离$q\bar{q} $势

Effective long distance $q\bar{q} $ potential in holographic RG flows

Jorge Casalderrey-Solana, Diego Gutiez, Carlos Hoyos

备注：
34 pages, 1 figure, new appendix with RG flow equation for the action and next order correction, references added, published version
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摘要：

利用全息术研究了强耦合非重整化群流的共形场论中的$q\bar{q}$势。我们专注于这个潜在的夸克间的分离$L$大的特性相比，规模的场论。这些都是由领先的IR物理加上一系列的修正，敏感的RG流的属性。为了确定这些修正，我们提出了一个一般的方法，应用全息威尔逊重整化的对偶弦。我们应用这种方法来详细研究两组例子，$3+1$维理论与RG流结束在一个IR固定点;和理论，限制在IR，特别是，Witten QCD和Klebanov-Strassler模型。在这两种情况下，我们发现与夸克间分离的普遍依赖的校正。当存在IR固定点时，该校正作为幂$\sim 1/L^4$衰减。我们解释了在一维缺陷理论的双迹变形的依赖。对于限制理论，衰减是指数的$\sim e^{-ML}$，其中$M$是胶球质量数量级的尺度。我们解释这个校正使用一个有效的通量管描述所产生的背景内部模式激发本地化的源在通量管的端点。我们将讨论如何将这些结果与格点QCD数据进行比较，以检验通过规范/引力对禁闭的描述是否定性正确。

英文摘要：

We study the $q\bar{q}$ potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. We focus on the properties of this potential at an inter-quark separation $L$ large compared to the characteristic scale of the field theory. These are determined by the leading order IR physics plus a series of corrections, sensitive to the properties of the RG-flow. To determine those corrections, we propose a general method applying holographic Wilsonian renormalization to a dual string. We apply this method to examine in detail two sets of examples, $3+1$-dimensional theories with an RG flow ending in an IR fixed point; and theories that are confining in the IR, in particular, the Witten QCD and Klebanov-Strassler models. In both cases, we find corrections with a universal dependence on the inter-quark separation. When there is an IR fixed point, that correction decays as a power $\sim 1/L^4$. We explain that dependence in terms of a double-trace deformation in a one-dimensional defect theory. For a confining theory, the decay is exponential $\sim e^{-ML}$, with $M$ a scale of the order of the glueball mass. We interpret this correction using an effective flux tube description as produced by a background internal mode excitation induced by sources localized at the endpoints of the flux tube. We discuss how these results could be confronted with lattice QCD data to test whether the description of confinement via the gauge/gravity is qualitatively correct.

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