Tachyon condensation and quark mass in the modified Sakai-Sugimoto model
Tachyon condensation and quark mass in the modified Sakai-Sugimoto model
复制标题
改进的 Sakai-Sugimoto 模型中的快子凝聚和夸克质量
DOI：
10.1103/physrevd.78.066021
复制
发表时间：
2008
影响因子：
5
通讯作者：
P. Nag
中科院分区：
文献类型：
--
作者：
A. Dhar;P. Nag
本文继续研究先前提出的改进 Sakai-Sugimoto 模型 [J.高能物理。 01（2008）055]。在这里，我们详细讨论膜轮廓和快子凝聚体的经典方程的数值解。事实证明，紫外线截止是必不可少的，因为数值解往往会迅速偏离所需的渐近解，超出全息坐标的足够大的值。所需的截止值由快子的不可归一化部分决定，并且在参数上远小于十维体积重力描述的一致性所规定的截止值。我们曾争论过[J.高能物理。 01 (2008) 055] 膜与反膜交汇点处的快子场趋于无穷大的解只有一个自由参数，可将其视为渐近膜-反膜分离。在这里，我们提供了支持这一观察结果的数字证据。我们还提供了证据，证明渐进快子解的不可归一化部分（在类 QCD 边界理论中用夸克质量来标识）是由该参数确定的。我们证明，渐进快子解的可归一化部分决定了夸克凝聚，但这还需要对壳上边界膜作用进行全息重整，因为存在无限的截止相关项。我们的重正化方案给出了对夸克质量截止的指数依赖性。我们还详细讨论了介子光谱，并表明当小夸克质量开启时，π介子质量不为零并且满足盖尔-曼-奥克斯-雷纳关系。« less
This paper continues the investigation of the modified Sakai-Sugimoto model proposed previously [J. High Energy Phys. 01 (2008) 055]. Here we discuss in detail numerical solutions to the classical equations for the brane profile and the tachyon condensate. An ultraviolet cutoff turns out to be essential because the numerical solutions tend to rapidly diverge from the desired asymptotic solutions, beyond a sufficiently large value of the holographic coordinate. The required cutoff is determined by the non-normalizable part of the tachyon and is parametrically far smaller than that dictated by consistency of a description in terms of ten-dimensional bulk gravity. We had argued [J. High Energy Phys. 01 (2008) 055] that the solution in which the tachyon field goes to infinity at the point where the brane and antibrane meet has only one free parameter, which may be taken to be the asymptotic brane-antibrane separation. Here we present numerical evidence in favor of this observation. We also present evidence that the non-normalizable part of the asymptotic tachyon solution, which is identified with quark mass in the QCD-like boundary theory, is determined by this parameter. We show that the normalizable part of the asymptotic tachyon solution determines the quark condensate, but thismore » requires holographic renormalization of the on-shell boundary brane action because of the presence of infinite cutoff-dependent terms. Our renormalization scheme gives an exponential dependence on the cutoff to the quark mass. We also discuss meson spectra in detail and show that the pion mass is nonzero and satisfies the Gell-Mann-Oakes-Renner relation when a small quark mass is switched on.« less