Bootstrapping One Theory and Bootstrapping All Theories

场论是我们理解自然界所有四种已知力的核心：电磁力、弱力、强力以及引力。此外，我们统一量子理论和引力的最佳候选者——弦理论——本身就是通过所谓的规范/弦二象性的量子场论来定义的。（这些值得注意的对应说明了某些量子场论和弦理论在弯曲时空中具有一个额外的空间维度之间的精确等价。）尽管规范理论在物理学中发挥着绝对的核心作用，但我们目前的理论工具还远远不能驯服它们。对约束、手性对称破缺和质量间隙的存在等物理现象的数学上合理的解析描述是根本不可用的，规范/弦二象性产生的精确场论机制仍然难以捉摸。为了解决这些令人着迷的问题，人们需要控制强耦合状态下的量子场理论，而标准的微扰技术在这方面是不够的。迫切需要新的概念方法和工具。到目前为止，我的主要研究正是集中在开发这样的工具上。在接下来的五年里，我和我的学员将研究非微扰量子场论中有限耦合下的相关函数和散射振幅的动态量。我们将使用N=4超杨-米尔斯理论——量子色动力学的超对称表亲——作为我们探索的一个关键主题。全息术和可积性是我们将大量使用的两个现代工具。我们将在这一理论中寻找最有趣的相关因素，正是那些迄今为止在分析描述方面所做的一切努力。我们还将考虑一种互补的方法，即我们探索与物理学中最神圣的原理（如单一性、相对性和局部性）相容的所有可能的量子场论的空间。这就是所谓的s矩阵自举程序我们最近重新使用了它。我们最近观察到，最令人兴奋的物理理论——尤其是那些描述现实世界现象的理论——似乎恰恰是那些生活在一致理论空间边界上的理论，也就是在可能与不可能之间的边界上。我们计划将s矩阵自举扩展为一种成熟的非微扰替代量子场论中通常局限于弱耦合系统的传统方法。就应用而言，很难估计一个理论研究项目在量子场论和弦理论中的广泛影响。当然，如果历史对我们有利的话，我们可以肯定，今天基础物理学的发展，尽管听起来很理论化，但将成为明天技术的核心

Field theory lies at the heart of our understanding of all four known forces in nature: the electromagnetic, weak and strong forces as well as gravity. Moreover, our best candidate for uniting quantum theory and gravity - string theory - is itself best defined through a quantum field theory by means of the so-called gauge/string dualities. (These are remarkable correspondences stating the precise equivalence between certain quantum field 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 quantum field 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. For the next five years, my trainees and I will investigate dynamical quantities known as Correlation Functions and Scattering Amplitudes at finite coupling in non-perturbative quantum field theories. We shall use N=4 super Yang-Mills theory - a supersymmetric cousin of quantum chromodynamics - as a key subject of our explorations. Holography and Integrability are two modern tools which we shall use intensively. We will look for the most interesting correlators in this theory, precisely those which have thus far evaded all efforts at an analytic description. We will also consider a complementary approach whereby we explore instead the space of all possible quantum field theories compatible with the most sacrosanct principles in physics such as unitarity, relativity and locality. This is the so called S-matrix bootstrap program which we recently revived. We have recently observed that the most exciting physical theories - and in particular those describing real world phenomena - seem to be precisely those living at the boundary of the space of consistent theories, so right at the boundary between the possible and the impossible. We plan to extend the S-matrix bootstrap into a full fledged non-perturbative alternative to conventional methods in quantum field theory which are normally limited to weakly coupled systems.   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