The Integrable Chromodynamic Flux Tube

规范理论是我们理解自然界四种已知力中的三种力的核心：电磁力、弱力和强力。此外，我们把量子理论和引力统一起来的最佳候选者--弦理论--本身最好是通过规范理论用所谓的规范/弦对偶来定义。（这些是显著的对应关系，说明了某些规范理论与具有一个额外空间维的弯曲时空中的弦理论之间的精确等价性。）尽管规范理论在物理学中扮演着绝对的核心角色，但它们还远远没有被我们目前的理论工具所驯服。一个数学上健全的物理现象，如禁闭，手征对称破缺和质量间隙的存在是根本没有可用的分析描述和精确的场论机制，规范/弦对偶来了仍然是难以捉摸的。为了解决这些迷人的问题，人们需要在强耦合区域控制规范理论，在那里标准微扰技术不足。迫切需要新的概念方法和工具。 到目前为止，我的主要研究一直集中在开发这样的工具，特别是，旨在提供第一个非微扰解的四维规范理论。我的研究计划在未来五年将集中在研究动态量称为相关函数，威尔逊环和散射振幅在有限耦合的非阿贝尔规范理论。我们将使用N=4的超杨-米尔斯理论--量子色动力学的超对称表亲--作为我们探索的主要课题。我们也希望从这种分析中吸取教训，这些教训将适用于一般的规范理论。全息论和可积性是我们将集中使用的两个现代工具。有了它们，我们就可以驯服这一卓越理论的色动力学通量管，并把它用于计算上面提到的动力学观测量。 就应用而言，很难估计量子场论和弦理论的理论研究计划的更广泛影响。当然，如果历史对我们有用，我们可以肯定，今天基础物理学的发展，尽管听起来是理论上的，但将成为明天技术的核心。

Gauge theories lie at the heart of our understanding of three of the four known forces in nature: the electromagnetic, weak and strong forces. Moreover, our best candidate for uniting quantum theory and gravity – string theory – is itself best defined through a gauge theory by means of the so-called gauge/string dualities. (These are remarkable correspondences stating the precise equivalence between certain gauge theories and string theories in curved space-times with one extra spatial dimension.) Despite their absolutely central role in physics, gauge theories are very far from being tamed with our current theoretical tools. A mathematically sound analytic description of physical phenomena such as confinement, chiral symmetric breaking and the existence of a mass gap is simply not available and the precise field theory mechanism by which gauge/string dualities come about is still elusive. To address these fascinating questions, one needs control over gauge theories in the strongly coupled regime, where standard perturbative techniques fall short. New conceptual approaches and tools are urgently needed. My main research thus far has been precisely focused on developing such tools and, in particular, has aimed at providing the first non-perturbative solution to a four dimensional gauge theory. My research program for the next five years will be focused on studying dynamical quantities known as Correlation Functions, Wilson loops and Scattering Amplitudes at finite coupling in non-abelian gauge theories. We shall use N=4 super Yang-Mills theory - a supersymmetric cousin of quantum chromodynamics - as the main subject of our explorations. We also hope to draw lessons from this analysis that will apply to gauge theories in general. Holography and Integrability are two modern tools which we shall use intensively. With them we shall tame the chromodynamic flux tube of this remarkable theory and put it to use in the computation of the dynamical observables mentioned above.  As far as applications go, it is very hard to estimate the broader impact a theoretical research program in quantum field theory and string theory. Of course, if history serves us well, we can be certain that today’s developments in fundamental physics, theoretical as they might sound, will lie at the very heart of tomorrow’s technology.