Tensor quantum field theories and the large N expansion

张量量子场论和大N展开

• 批准号: 2396767
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2396767
• 关键词: Tensor; quantum; field; theories; large

This is a project in theoretical particle physics. It addresses questions in the STFC themesWhat are the fundamental particles and fields? and What are the fundamental laws and symmetries of physics? Quantum field theory is the framework within which the answers to these questions can be investigated. We are far from knowing all the consistent quantum field theories, especially beyond perturbation theory, and understanding their renormalisation group fixed-point structure and phases. The large N expansion is a method of accessing some kinds of non-perturbative structure; used in model field theories it enables us to establish, for example, the existence of potentially non-trivial conformal field theories which have no known direct Lagrangian formulation.Tensor field theories, both bosonic and fermionic, have been studied recently in the context of the large N limit in three space-time dimensions where they are typically dominated by so-called melonic diagrams. Their direct product symmetry groups lead to theories with a (very large in some cases) number of coupling constants which in turn leads to a potentially complicated phase diagram with an intricate RG structure consisting of many fixed points and potentially lines of fixed points. They are thus good laboratories for identifying new CFTs. This project will study two aspects of these theories.The large number of coupling constants in theories containing a scalar field with a multiple-index internal symmetry has been dealt with in some cases by truncating to a self-consistent subset of more manageable size. However it is not known whether this subset is stable against addition of extra directions in the full coupling constant space or indeed whether there are other self-consistent choices which lead to substantially different RG structures. There are at least two approaches to this problem and the project will pursue both. The first is brute force: the large number of degrees of freedom cannot be managed by hand and the calculations have to be automated. However even automated calculations can proliferate rapidly in size and establishing the best basis in which to work using conventional symbolic mathematics systems is already a challenge. A speculative line which may turn out to be more powerful ultimately is the recent emergence of deep learning for symbolic mathematics; at present work in this area is on integration and differentiation but exploring a high dimensional space seems a natural candidate for deep learning. The second approach to the problem is to identify hidden symmetries that forbid the generation of paths into the extra directions, for example by generating the model from some underlying theory in which the symmetry is explicit.

这是一个理论粒子物理学的项目。它解决了STFC主题中的问题：什么是基本粒子和场？物理学的基本定律和对称性是什么？量子场论是可以研究这些问题的答案的框架。我们还远未了解所有的相容量子场论，特别是微扰论之外的理论，也远未了解它们的重整化群不动点结构和相位。大N展开式是一种获取某些非微扰结构的方法;在模型场论中，它使我们能够建立，例如，没有已知的直接拉格朗日公式的潜在非平凡共形场论的存在。张量场论，玻色子和费米子，最近已经研究了大N极限的背景下，在三个时空维度，他们通常是由所谓的melonic图为主。他们的直积对称群导致理论与（在某些情况下非常大）数量的耦合常数，这反过来又导致一个潜在的复杂的相图与复杂的RG结构组成的许多固定点和潜在的线的固定点。因此，它们是确定新的CFTs的良好实验室。本计画将研究这些理论的两个方面：在含有多指数内对称标量场的理论中，大量的耦合常数在某些情况下已被截断成一个更易于处理的自洽子集。然而，它是不知道这个子集是否是稳定的，对增加额外的方向在全耦合常数空间，或者确实是否有其他自洽的选择，导致实质上不同的RG结构。至少有两种方法可以解决这个问题，本项目将同时采用这两种方法。第一个是蛮力：大量的自由度无法手动管理，计算必须自动化。然而，即使是自动计算也可以在规模上迅速扩散，并且使用传统的符号数学系统建立最佳基础已经是一个挑战。一条最终可能变得更强大的推测路线是最近出现的符号数学深度学习;目前这一领域的工作是积分和微分，但探索高维空间似乎是深度学习的自然候选者。解决这个问题的第二种方法是识别隐藏的对称性，这些对称性禁止生成进入额外方向的路径，例如通过从一些基本理论生成模型，其中对称性是明确的。