Chiral Gauge Theories: From Strong Coupling to the Standard Model

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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.