Running Coupling and Beta-Functions for HQCD with Heavy and Light Quarks: Isotropic case
Running Coupling and Beta-Functions for HQCD with Heavy and Light Quarks: Isotropic case
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运行重夸克和轻夸克 HQCD 的耦合和 Beta 函数：各向同性情况
DOI：
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发表时间：
2024
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通讯作者：
Marina Usova
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作者：
I. Aref’eva;A. Hajilou;P. Slepov;Marina Usova
我们考虑在重夸克和轻夸克的爱因斯坦-膨胀-麦克斯韦作用支持的全息模型中运行耦合常数和β函数。为了获得运行耦合常数 $\alpha$ 对温度和化学势的依赖性，我们对取决于地平线位置的膨胀场施加边界条件。我们使用两种类型的边界条件：一种是膨胀场在地平线消失的简单边界条件，另一种是确保与零化学势夸克之间弦张力的晶格计算一致的边界条件。 $(T,\mu)$平面中的一阶相变的位置不依赖于轻夸克和重夸克的膨胀边界条件。在这些相变中，函数 $\alpha$ 和 $\beta$ 根据温度和化学势发生跳跃。我们还表明，对于第二个边界条件，运行耦合随着温度的升高而降低，并且轻夸克和重夸克对温度和化学势的依赖性实际上是由一个变量的函数指定的，从这个意义上证明了自动模型行为。
We consider running coupling constant and beta-function in holographic models supported by Einstein-dilaton-Maxwell action for heavy and light quarks. To obtain the dependence of the running coupling constant $\alpha$ on temperature and chemical potential we impose boundary conditions on the dilaton field that depend on the position of the horizon. We use two types of boundary conditions: a simple boundary condition with the dilaton field vanishing at the horizon, and a boundary condition that ensures agreement with lattice calculations of string tension between quarks at zero chemical potential. The location of the first-order phase transitions in $(T,\mu)$-plane does not depend on the dilaton boundary conditions for light and heavy quarks. At these phase transitions, the functions $\alpha$ and $\beta$ undergo jumps depending on temperature and chemical potential. We also show that for the second boundary conditions the running coupling decreases with increasing temperature and the dependence on temperature and chemical potential for both light and heavy quarks are actually specified by functions of one variable, demonstrating in this sense auto-model behavior.