Solving thermal QCD using string theory techniques

过去几年我在麦吉尔大学的研究方向一直是强耦合规范理论，比如量子色动力学（QCD）。特别是，我试图对这些理论进行一些分析控制。显然，标准的微扰技术，如费曼图，对分析这些理论是没有用的，因为它们之间存在强相互作用。在“颜色”数N变大的极限下，弦理论领域的一项新发展表明，这些理论可能存在双重引力描述，其中所有非微扰物理都可以简单地使用经典超引力技术进行分析！在过去的几年里，我们已经能够开发一个纯粹使用超重力技术的模型，以模拟低能量和高能量的大N热QCD。我们已经用这个模型计算了热QCD的许多可观测物理，即剪切粘度、熵、QGP相、约束和非约束动力学、夸克元熔化等。毫无疑问，这些发展是及时的，在接下来的几年里，我想把我的时间花在进一步发展这幅画上，并将其扩展到彩色超导阶段。大N热QCD和彩色超导的物理性质有惊人的相似之处，我们在这里开发的引力描述可能用于进一步研究。此外，我们所建立的模型在高能量下也表现良好。这是我认为在文献中提出的许多其他模型中所缺少的一个优势。标准QCD的高能行为很简单：它是一个几乎自由的理论。在大颜色极限中，即在大N极限中，高能行为是共形的，或者说是尺度不变的。这正是我们的模型在高能量下的表现。在引力对偶中，高能行为被大半径区域捕获，低能行为被小半径区域捕获。然而，完整的引力对偶解仍然没有被构造出来，我的长期目标之一是完成这幅图。这个练习在技术上是具有挑战性的，但我相信在我的研究生的努力和帮助下，我们应该能够完成双重描述。一旦确定了对偶描述，分析出QCD的各种性质将是非常有趣的，这些性质是用以前的技术无法解决的。我的第二个建议是研究最近引起一些兴趣的宇宙学的某些方面。有一段时间，人们认为弦理论很容易产生德西特真空，只要某些不存在的条件被违反。我们还提出了一个候选解，该解考虑了各种非摄动效应，这至少为我们研究弦理论中的de-Sitter解提供了一种方法，尽管没有构造显式解。但是，最近提出了关于这一办法的某些问题。我明年的目标之一就是解决这个问题。这在技术上是一项具有挑战性的工作，因为弦理论中导致宇宙加速的显式超重力解很难构建。如果成功，这可能是第一个与时间相关的超重力解的非平凡例子。我的第三个建议是详细阐述最近在异质弦理论中提出的规范/重力对偶，其中我们给出了一个规范理论的重力对偶，其场论描述是完全神秘的。我的目标是通过我们提出的对偶来了解这个理论。最后，我的第四个建议是使用弦理论的技术扩展新发现的共形Seiberg-Witten型规范理论。

My research directions at McGill in the last few years have been along strongly coupled gauge theories, an example being Quantum Chromodynamics (QCD). In particular I have attempted to have some analytical control over these theories. Clearly standard perturbative techniques, like Feynman diagrams, are not useful to analyze these theories because of strong interactions. In the limit where the number of "colors" N is made large, a new development in the field of string theory has shown that there could be a dual gravitational description of these theories wherein all the non-perturbative physics can be analyzed simply using classical supergravity techniques! In the past few years we have been able to develop a model purely using supergravity techniques that mimic large N thermal QCD both at low and high energies. We have been using this model to compute many observable physics of thermal QCD, namely shear viscosity, entropy, QGP phase, confinement and deconfinement dynamics, quarkonium melting etc. These developments are timely no doubt and for the next few years I want to devote my time to develop the picture further and extend this to the color superconductivity phase. The physics of large N thermal QCD and color superconductivity have amazing similarities, and the gravitational description that we have developed here could probably be used to study this further. Additionally, the model that we have developed behave well at high energies too. This is one advantage that I believe is missing in many of the other models proposed in the literature. The high energy behavior of standard QCD is simple: it is an almost free theory. In the large color limit i.e in the large N limit, the high energy behavior is conformal or alternatively, scale-invariant. This is exactly how our model behaves at high energies. In the gravitational dual, the high energy behavior is captured by the regions at large radius and the low energy behavior is captured by the regions at small radius. However the full gravitational dual solution is still not been constructed, and one of my long term aim would be to complete this picture. The exercise is technically challenging, but I believe that with efforts and with the help of my graduate students, we should be able to complete the dual description. Once the dual description is laid out, it will be very interesting to work out analytically the various properties of QCD which were impossible to solve using previous techniques. My second proposal is to work on certain aspects of cosmology that has recently generated some interest. For sometime it was thought that string theory would easily generate de-Sitter type vacua provided certain no-go conditions were violated. A candidate solution was also proposed that took into account various non-perturbative effects that gave us a way at least to study de-Sitter solutions in string theory, although no explicit solutions were constructed. However, recently, certain issues were raised regarding this approach. One of my aim for next year or so would be to resolve this issue. This is a technically challenging exercise as explicit supergravity solutions in string theory that give rise to accelerating universe is very hard to construct. If successful, this would probably be the first non-trivial example of a time-dependent supergravity solution. My third proposal would be to elaborate on the recently proposed gauge/gravity duality in heterotic string theory wherein we gave the gravity dual for a gauge theory whose field theory description was completely mysterious. My aim would be to learn about this theory using our proposed dual. Finally, my fourth proposal would be to extend the newly found conformal Seiberg-Witten type gauge theories using techniques of string theory.