Chiral Gauge Theories: From Strong Coupling to the Standard Model

在电影《黑客帝国》（the Matrix）中，角色尼奥（Neo）逐渐意识到，他周围的世界只不过是一台功能强大的电脑（比如Playstation 137）中的模拟世界。值得注意的是，有一个数学定理说这在我们的世界里是不可能的。在20世纪80年代被证明的尼尔森-尼诺米亚定理说，原则上，在计算机上模拟已知的物理定律是不可能的。当然我们不知道该怎么做。从表面上看，尼尔森-尼诺米亚定理表明，也没有其他人能做到这一点。然而，物理学中的“不去”定理只有在它们的假设下才有效。在某种程度上，这个项目的目的是探索尼尔森-尼诺米亚定理中可能存在的漏洞，并找到一种在计算机上模拟物理定律的方法。更广泛地说，这个项目的目的是研究我们生活的世界中一些最微妙和最有趣的方面。大约75年前，伟大的实验家吴建雄发现了这些微妙的方面。她表明，在基本层面上，我们所观察到的物理定律在镜子中反映出来时看起来是不同的。当然，在日常生活中，通常很容易分辨出你是在看原始图像还是它的反射。字迹变得难以辨认，熟悉的面孔看起来令人不安地奇怪。但令人惊讶的是，这在亚原子粒子的水平上仍然成立。即使在最小的水平上，如果你足够近地观察亚原子反应，你也能分辨出你是在看原始反应还是在看反射反应。经过75年的后见之明，很明显，这个听起来无害的结果是我们所知道的关于自然的最深刻的事实之一。那些在镜子里看起来不一样的物理理论被称为“手性”，具有许多微妙而令人惊讶的特性，与数学中的拓扑和几何思想有关。在这些令人惊讶的性质中，最突出的是尼尔森-尼诺米亚定理，该定理指出，没有办法在计算机上模拟手性量子理论。它们太微妙，太强硬。任何计算机都将拒绝计算。这个项目将探索手性量子理论的性质。描述基本粒子的粒子物理标准模型是迄今为止最有趣的，但从宏观上看并尝试学习所有的手性理论通常是值得的。我们的目标是揭示手性这一神秘现象，从而更好地理解我们所生活的宇宙。最终，雄心勃勃的目标是看看是否有可能逃避尼尔森-尼诺米亚定理，并在计算机上模拟物理定律。该项目不会解决我们是否生活在母体中的问题。这个问题最好留给那些看了太多90年代电影的纸上谈兵的哲学家。

In the movie The Matrix, the character Neo comes to learn that the world around him is nothing more than a simulation in some extraordinarily powerful computer, say a Playstation 137.Remarkably, there is a mathematical theorem that says this cannot be the case in our world. The Nielsen-Ninomiya theorem, proven in the 1980s, says that it is not, in principle, possible to simulate the known laws of physics on a computer. Certainly we don't know how to do it. Taken at face value, the Nielsen-Ninomiya theorem says that no one else could do it either.However, no-go theorems in physics are only as good as their assumptions. In part, the purpose of this project is to explore the possible loopholes in the Nielsen-Ninomiya theorem and find a way to simulate the laws of physics on a computer. More broadly, the purpose of the project is to study some of the most subtle and interesting aspects of the world we live in. These subtle aspects were discovered almost 75 years ago by the great experimenter Chien-Shiung Wu. She showed that, at the fundamental level, the laws of physics we observe look different when reflected in a mirror. Of course, in every day life it is often straightforward to tell if you're looking at an original image or at its reflection. Writing becomes illegible, familiar faces look disconcertingly peculiar. But it is surprising that this continues to hold at the level of subatomic particles. Even at the smallest level, if you stare at a subatomic reaction closely enough, you can tell if you're looking at the original or looking at the reflection. With 75 years of hindsight, it is clear that this innocuous sounding result is one of the deepest facts we know about Nature. Theories of physics that look different when reflected in the mirror are said to be "chiral" and have many subtle and surprising properties, connected to ideas of topology and geometry in mathematics. Prominent among these surprising properties is the Nielsen-Ninomiya theorem which states that there is no way to simulate chiral quantum theories on a computer. They are too subtle, too hard. Any computer will simply refuse to compute.This project will explore the properties of chiral quantum theories. The Standard Model of particle physics that describe fundamental particles is, by far, the most interesting of these, but it often pays to look at the big picture and try to learn about all chiral theories. The goal is to shed light on this mysterious phenomenon of chirality and, in doing so, better understand the universe we live in. The ultimate, ambitious, goal is to see if perhaps it is possible to evade the Nielsen-Ninomiya theorem and simulate the laws of physics on a computer. The project will not address the question of whether we live in the Matrix. That is best left to armchair philosophers who have watched too many 90s movies.