通过相变约束优化全息QCD中的膨胀子势
Optimizing the dilaton potential in holographic QCD via phase-transition constraints
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中文总结 AI 辅助
本文提出通过相变约束优化膨胀子势，构造能重现重建方法相变特征的最小势模型，在轻夸克模型中恢复一阶相变线、类Cornell势及禁闭交叉位置。
中文摘要 AI 辅助
在自下而上的全息QCD（HQCD）中，通常采用两种主要方法：势重建方法（其中背景几何预先固定，膨胀子势由此导出）和直接方法（其中势被明确指定）。虽然重建方法在捕捉极端条件下QCD的现象学性质方面非常有效，但存在一个微妙问题：重建的势依赖于所选择的全息边界条件。为解决此问题，我们提出构造一个膨胀子势，旨在重现通过重建方法获得的HQCD相变的典型特征，而非仅从HQCD真空解导出。以轻夸克模型为例，我们构造了一个能捕捉该模型相结构主要特征的势。其参数在零化学势下通过最小化直接模型与重建模型中视界位置对温度依赖性的偏差，并拟合到相同的临界端点（CEP）位置来确定。所得的最小势模型即使在相对较小的化学势下也能令人满意地恢复轻夸克模型的物理。具体而言，它产生的一阶相变（FOPT）线接近通过重建方法获得的线。此外，最小势模型重现了上升的类Cornell夸克-反夸克势，直至强子距离$\ell=1.5$ fm，我们将其用作禁闭的现象学有限距离判据。该最小势模型中禁闭/退禁闭交叉的位置也接近原始轻夸克模型中的对应位置。
英文摘要
In bottom-up holographic QCD (HQCD), two primary approaches are commonly employed: the potential reconstruction method, where the background geometry is fixed a priori and the dilaton potential is derived, and the direct method, where the potential is specified explicitly. While the reconstruction method is highly effective for capturing the phenomenological properties of QCD under extreme conditions, a subtlety arises in that the reconstructed potential depends on the chosen holographic boundary conditions. To address this issue, we propose constructing a dilaton potential designed to reproduce the typical features of HQCD phase transitions obtained by the reconstruction method, rather than one derived solely from HQCD vacuum solution. Using a light-quark model as an example, we construct a potential that captures the principal features of the phase structure of this model. Its parameters are determined at zero chemical potential by minimizing the deviation between the temperature dependence on the horizon position in the direct and reconstructed models and by fitting to the same position of a critical endpoint (CEP). The resulting minimal-potential model satisfactorily recovers the physics of the light-quark model even at relatively small chemical potential. Specifically, it yields a first-order phase transition (FOPT) line close to those obtained from the reconstruction method. Additionally, the minimal-potential model reproduces a rising Cornell-like quark-antiquark potential up to the hadronic distance $\ell=1.5$ fm, which we use as a phenomenological finite-distance criterion for confinement. The location of the confinement/deconfinement crossover in this minimal-potential model is also close to its counterpart in the original light-quark model.
