On Conformal Field Theory and Dark Matter

论共形场论和暗物质

• 批准号: SAPIN-2020-00038
• 负责人: Fortin, JeanFrancois
• 金额: $ 2.91万
• 依托单位: Université Laval
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=718637
• 关键词: Conformal; Field; Theory; Dark; Matter

The two pillars of modern theoretical physics are quantum mechanics and general relativity. Although they cannot be combined together into a consistent framework yet (a notable exception being string theory), the union of quantum mechanics and special relativity, the basis for general relativity, leads to a consistent framework. This framework, called quantum field theory, gives rise to the most precise theory of elementary particles found thus far. However, there are many open questions concerning the formal aspects of quantum field theory or its use in particle physics that are still unanswered. The research proposal focuses on two different aspects of quantum field theory: conformal field theory and dark matter. 1) One of the most important discoveries in physics of the twentieth century, the renormalization group, is an unavoidable consequence of quantum field theory. The renormalization group, which is an iterative process where high-momentum degrees of freedom are integrated out, generates a flow in the space of all theories which determines the changes a physical system undergoes as viewed at different distance scales. It is of paramount importance in modern physics, especially in quantum field theory and condensed matter physics, since it allows the study of long-distance physics (emergent phenomena) through universality classes. Conformal field theories are theories that live at fixed points of the renormalization group flow. Their symmetry group is extended and the extra symmetries give a better handle on the typical observables present in conformal field theory. By themselves, consistency conditions originating from conformal invariance could be enough to solve the theories, and the first part of the research proposal aims to tackle this problem. Conformal field theories have applications in several areas of research including string theory and second-order phase transitions in condensed matter physics. A better understanding of conformal invariance could have far-reaching consequences, leading to a complete classification of all quantum field theories in terms of relevant deformations of conformal field theories. 2) Although the standard model of particle physics, based on quantum field theory, successfully explains a host of observations, unsolved questions remain. Dark matter, introduced to account for the missing mass inferred from astrophysical observations (for example from orbital speed measurements of visible stars in galaxies), is one such unexplained conundrum. The second part of the research proposal focuses on the issue of dark matter by investigating astrophysical constraints on dark matter models of weakly-interacting and very light hypothetical particles. These particles are well-motivated theoretically and lead to viable candidates for dark matter. Understanding the puzzle associated with dark matter could lead to a better understanding of our Universe and answer some of our most profound questions about it.

现代理论物理学的两大支柱是量子力学和广义相对论。尽管它们还不能组合成一个一致的框架（弦理论是一个值得注意的例外），但量子力学和狭义相对论（广义相对论的基础）的结合导致了一个一致的框架。这个被称为量子场论的框架产生了迄今为止发现的最精确的基本粒子理论。然而，关于量子场论的形式方面或其在粒子物理学中的应用，还有许多悬而未决的问题尚未得到解答。 该研究计划重点关注量子场论的两个不同方面：共形场论和暗物质。 1）二十世纪物理学中最重要的发现之一，重整化群，是量子场论不可避免的结果。重正化群是一个迭代过程，其中高动量自由度被积分出来，在所有理论的空间中产生一个流，该流决定了物理系统在不同距离尺度上所经历的变化。它在现代物理学中至关重要，特别是在量子场论和凝聚态物理学中，因为它允许通过普适性类来研究长距离物理（涌现现象）。共形场论是存在于重整化群流的固定点的理论。它们的对称群得到了扩展，额外的对称性可以更好地处理共形场论中存在的典型可观测量。就其本身而言，源自共形不变性的一致性条件足以解决该理论，并且该研究提案的第一部分旨在解决这个问题。共形场论在多个研究领域都有应用，包括弦理论和凝聚态物理中的二阶相变。对共形不变性的更好理解可能会产生深远的影响，从而根据共形场论的相关变形对所有量子场论进行完整的分类。 2）虽然基于量子场论的粒子物理标准模型成功地解释了许多观察结果，但仍然存在未解决的问题。暗物质的引入是为了解释天体物理观测（例如通过星系中可见恒星的轨道速度测量）推断出的缺失质量，就是这样一个无法解释的难题。该研究计划的第二部分通过研究弱相互作用和极轻假设粒子的暗物质模型的天体物理约束来关注暗物质问题。这些粒子在理论上具有良好的动机，并为暗物质提供了可行的候选者。了解与暗物质相关的谜题可以让我们更好地了解我们的宇宙，并回答一些关于它的最深刻的问题。