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

我的研究领域是弦理论，这是一种非常先进的理论构造，它允许所有自然力的统一。弦理论有不同的限制，在某些情况下主要是引力效应，而在另一些情况下则是场论效应。弦理论作为一种统一的自然理论的应用还不成熟，但这是一种非常令人兴奋的可能性。直到有一天我们可以使用弦来进行实验预测，我们才试图更好地理解这个理论，并试图从它身上学到理论物理中的其他问题。这是我在研究中追求的方向。如上所述，我们可以从弦理论中分离出一些用更简单的理论描述的子领域。尤其是所谓的规范理论(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很好地描述了(被称为“粒子物理的标准模型”)。这一理论可以通过相当复杂的构造在弦理论中实现。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。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的计算，并对结果进行比较，结果往往令人惊讶地一致。虽然这一理论在自然界中可能没有实现，但它在许多方面与粒子物理的标准模型相似。更好地理解这一理论应该会带来更好的粒子物理计算工具。虽然这一理论(在某些方面)比标准模型更简单，但它仍然相当丰富和复杂。我的具体研究集中在确定该理论的哪些部分可以获得确切的结果。有几个这样的界别分组是已知的(我也为他们的理解做出了贡献)，我研究的目的是找到更多这样的分组，更好地了解已知的界别分组，并将其扩大到包括更多可计算的数量。这条研究路线的最终目标是对这个理论有一个完整的理解，在这个理论中，所有的量都可以计算。这一目标目前似乎还远未实现，但过去几年取得的显著进展使人们对这一目标并非完全遥不可及抱有希望。无论我们是否达到这一目标，对这一理论的更好理解有望在理论物理中得到其他应用。它可以应用于弦理论的其他领域，甚至可以应用于凝聚态物理，凝聚态物理使用的一些工具与研究N=4杨-米尔斯时使用的工具相同。此外，它还有助于理解标准模型，特别是QCD，即强相互作用理论。这一理论是强耦合的，理解其他理论在强耦合下的表现也可以解释这一理论。

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.