Confinement and Conformality in Theories with Massless Fermions using Finite Volume Analysis

该奖项资助佛罗里达国际大学Rajamani Narayanan教授的研究活动。宇宙中的一切物质都是由基本粒子组成的。因此，物质的基本理论应该能够解释这些粒子的质量，包括质子和中子的质量，它们反过来又支配着原子、固体、液体和气体的质量。量子色动力学（QCD）是描述质子和中子以及其他粒子的理论。然而，QCD的基本组成部分不是质子和中子，而是被称为夸克和胶子的更小的组成粒子，它们都是无质量的。QCD是如何用无质量的夸克和胶子来描述大质量的质子和中子的，这是物理学中一个重要的基本问题，回答这个问题可以对美国的科学进步产生重大影响。事实证明，QCD有两个参数：夸克的种类数量（称为“口味”）和胶子的数量（称为“颜色”）。根据这两个数字的选择，理论可以分为两类：一类只产生无质量粒子，另一类产生大量有质量粒子。作为研究的一部分，纳拉亚南教授将对这两类理论进行计算机密集型研究。该研究项目还预计将产生更广泛的重大影响。计算技能在当今的工作中是必不可少的，与PI一起进行这项研究的学生将发展这些技能，使他们能够在学术界或工业界从事职业。从技术上讲，QCD是一种在经典水平上具有尺度不变性的理论。根据口味和颜色的数量，尺度不变性在量子水平上保持不变，导致无质量粒子的光谱，或者在量子水平上被打破，产生一个尺度，导致有质量粒子的光谱。用于研究与无质量费米子耦合的规范场的晶格形式是提取这些理论的基本非微扰性质的一种久经考验的方法。Narayanan教授将使用晶格形式来研究有限周期盒中潜在的尺度不变理论。盒子的大小设定了一个外部尺度，Narayanan教授计划通过研究作为外部尺度函数的渐近行为来提取该理论的尺度不变特性。这项研究的结果将在国际会议上发表，并在同行评议的期刊上发表。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award funds the research activities of Professor Rajamani Narayanan at Florida International University.All matter in the universe is composed of fundamental particles. Accordingly, a fundamental theory of matter should be able to explain the masses of these particles, including the masses of protons and neutrons which in turn dominate the masses of atoms, solids, liquids, and gases. Quantum Chromo Dynamics (QCD) is the theory that describes these protons and neutrons, among other particles. However, the fundamental building blocks of QCD are not protons and neutrons, but smaller constituent particles known as quarks and gluons, all of which are massless. How QCD ends up describing massive protons and neutrons in terms of massless quarks and gluons is therefore an important basic question in physics, and answering this question can have significant ramifications for the progress of science in the United States. It turns out that QCD has two parameters: the number of types of quarks (called "flavors") and number of gluons (called "colors"). Depending on the choices of these two numbers, theories fall into one of two categories: one category gives rise to only massless particles, and the other produces a rich spectrum of massive particles. As part of his research, Professor Narayanan will conduct computer-intensive studies of theories within both categories. This research project is also envisioned to have significant broader impacts. Computational skills are essential in today’s work, and students who work with the PI on this research will develop these skills, enabling them to have careers in either academics or industry.More technically, QCD is a theory that has scale invariance at the classical level. Depending on the number of flavors and colors, scale invariance is maintained at the quantum level, resulting in a spectrum of massless particles, or it is broken at the quantum level, generating a scale which results in a spectrum of massive particles. A lattice formalism for studying gauge fields coupled to massless fermions is a well-tested approach for the extraction of the fundamental non-perturbative properties of these theories. Professor Narayanan will use the lattice formalism to study potentially scale-invariant theories in a finite periodic box. The size of the box sets an external scale, and Professor Narayanan plans to extract the scale-invariant properties of the theory by studying the asymptotic behavior as a function of the external scale. Results of this research will be presented at international conferences and published in peer-reviewed journals.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.