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。虽然它们还不能结合成一个一致的框架（一个值得注意的例外是弦理论），但量子力学和狭义相对论的结合，广义相对论的基础，导致了一个一致的框架。这个框架，称为量子场论，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。 该研究计划侧重于量子场论的两个不同方面：共形场论和暗物质。1)重整化群是世纪物理学中最重要的发现之一，它是量子场论的必然结果。重整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动，它决定了物理系统在不同距离尺度上所经历的变化。它在现代物理学中是至关重要的，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学（涌现现象）。共形场论是存在于重整化群流的不动点的理论。他们的对称群是扩展和额外的对称性给出了一个更好的处理典型的观测存在于共形场论。由共形不变性产生的一致性条件本身就足以解决理论问题，研究计划的第一部分旨在解决这个问题。共形场论在几个研究领域都有应用，包括弦理论和凝聚态物理学中的二级相变。更好地理解共形不变性可能产生深远的影响，导致所有量子场论根据共形场论的相关变形进行完整的分类。2)尽管基于量子场论的粒子物理学标准模型成功地解释了大量的观测结果，但仍存在未解决的问题。暗物质是一个无法解释的难题，它被用来解释从天体物理学观测（例如从星系中可见恒星的轨道速度测量）中推断出的缺失质量。研究提案的第二部分侧重于暗物质问题，研究弱相互作用和非常轻的假设粒子的暗物质模型的天体物理约束。这些粒子在理论上有很好的动机，并导致暗物质的可行候选者。理解与暗物质相关的谜题可以更好地理解我们的宇宙，并回答我们关于它的一些最深刻的问题。