Precision calculations in field theories and in string theory and the relations between them

我的研究领域是弦理论，一种非常先进的理论结构，它允许所有自然力的统一。弦理论有不同的限制，在一些理论中，主导效应是引力，而在另一些理论中，它们是场理论。弦理论作为自然界的统一理论的应用还不成熟，但这是一个非常令人兴奋的可能性。直到有一天，我们可以用弦来做实验预测，我们试图更好地理解这个理论，并试图从中学习理论物理中的其他问题。这是我的研究方向。如上所述，我们可以从弦理论中分离出一些由更简单的理论描述的子部门。特别是所谓的规范理论（其中最简单的是电磁学）。亚原子粒子的领域被一个这样的理论（被称为“粒子物理学的标准模型”）很好地描述了。这个理论可以在弦理论中通过相当复杂的结构来实现。还有另一种规范理论，在弦理论中有一个非常简单的实现，通常被称为N=4超对称杨-米尔斯理论。这一理论在弦理论中的简单表现使我们能够在强耦合和弱耦合下进行精确计算，并比较结果，结果往往令人惊讶地一致。虽然这个理论可能无法在自然界中实现，但它在许多方面与粒子物理学的标准模型相似。对这一理论的更好理解将导致粒子物理学更好的计算工具。虽然这个理论（在某些方面）比标准模型更简单，但它仍然相当丰富和复杂。我的具体研究侧重于确定理论的子部门，在那里可以获得确切的结果。有几个这样的子行业是已知的（我对他们的理解做出了贡献），我研究的目的是找到更多这样的子行业，更好地理解已知的，并扩大它们以包括更多可计算的数量。这条研究路线的最终目标是对这一理论有一个完整的理解，所有的量都可以计算出来。目前看来，这一目标还远未实现，但在过去几年中已经取得了显著进展，这使人们相信这一目标并非完全无法实现。无论我们是否达到这个目标，对这一理论的更好理解都有望在理论物理学中有其他应用。它可以应用于弦理论的其他领域，甚至是凝聚态物理，它使用了一些研究N=4 Yang-Mills的相同工具。此外，它可以帮助理解标准模型，特别是QCD，强相互作用理论。这个理论是强耦合的，理解其他理论在强耦合下的表现也可以解释这个理论。

My field of research is string theory, a very advanced theoretical construct that allows for the unification of all the forces of nature. String theory has different limits, in some the dominant effects are gravitational and in others they are field-theoretical. The application of string theory as a unified theory of nature is not mature yet, but is a very exciting possibility. Until the day comes when we can use strings to make experimental predictions we try to gain a better understanding of the theory and try to learn from it about other questions in theoretical physics. That is the direction I pursue in my research. As stated above, we can isolate from string theory some subsectors, which are described by simpler theories. In particular, what are known as gauge theories (the simplest of which is elecro-magnetism). The realm of subatomic particles is well described by one such theory (know as ``the standard model of particle physics''). This theory can be realized in string theory by rather complicated constructions. There is another gauge theory with a beautifully simple realization in string theory, commonly known as N=4 supersymmetric Yang-Mills. The simple manifestation of this theory in string theory allows us to make precise calculations both at strong and weak coupling and compare the results, often with surprising agreement. While this theory is probably not realized in nature, it is similar in many ways to the standard model of particle physics. A better understanding of this theory should lead to better calculational tools for particle physics. While this theory is simpler (in some ways) than the standard model, it is still quite rich and complicated. My specific research focuses on identifying subsectors of the theory where exact results can be obtained. Several such subsectors are known (and I have contributed to their understanding) and the purpose of my research is to find more such subsectors, understand the known ones better and enlarge them to include more calculable quantities. The ultimate goal of this line of research is to have a complete understanding of this theory, where all quantities can be calculated. This goal seems quite far from being attained at the moment, but remarkable progress has been achieved over the past few years that gives hope that this goal is not completely out of reach. Whether we reach that target or not, a better understanding of this theory promises to have other applications in theoretical physics. It could have applications in other corners of string theory, or even for condensed matter physics, which uses some of the same tools used in studying N=4 Yang-Mills. Furthermore, it could help understand the standard model and in particular QCD, the theory of the strong interactions. That theory is strongly coupled and understanding how other theories behave at strong coupling could shed light on this theory too.