Bootstrapping One Theory and Bootstrapping All Theories

场论是我们理解自然界中已知的所有四种力的核心：电磁力、弱力和强力以及重力。此外，我们将量子理论和引力弦理论相结合的最佳候选者--弦理论--本身就是通过所谓的规范/弦对偶的量子场论来定义的。(这些惊人的对应说明了弯曲时空中某些量子场论和弦理论之间的精确等价性，空间维度增加了一个。)尽管规范理论在物理学中发挥着绝对的核心作用，但它远远不能被我们目前的理论工具所驯服。对于禁闭、手征对称破缺和质量间隙的存在等物理现象，还没有一个数学上合理的解析描述，而形成规范/弦对偶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，人们需要在强耦合区域控制量子场理论，在强耦合区域，标准微扰技术是不够的。迫切需要新的概念方法和工具。到目前为止，我的主要研究一直集中在开发这样的工具上。在接下来的五年里，我和我的受训人员将研究非微扰量子场论中被称为关联函数和有限耦合下的散射幅度的动量。我们将使用N=4的超杨-米尔斯理论--量子色动力学的一个超对称表亲--作为我们探索的一个关键主题。全息术和可积性是我们将广泛使用的两种现代工具。我们将在这一理论中寻找最有趣的关联者，正是那些迄今在分析描述中回避了所有努力的关联者。我们还将考虑一种互补的方法，通过这种方法，我们将探索所有可能的量子场论的空间，这些理论与物理学中最神圣的原则相兼容，例如一元性、相对论和局域性。这就是我们最近重新启动的所谓的S矩阵自举程序。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的边界上的理论，因此恰好处于可能和不可能之间。我们计划将S矩阵自举扩展为量子场论中常规方法的一个完全成熟的非微扰替代方法，这些方法通常仅限于弱耦合系统。但就应用而言，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，如果历史对我们有利，我们可以肯定，今天基础物理学的发展，尽管听起来可能是理论上的，但将成为未来技术的核心

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