Lattice Field Theory and Hadronic Physics

对非阿贝尔规范理论与不同规范群表示的费米子耦合的数值研究将构成本提案中所有项目的中心焦点。量子色动力学(QCD)属于我们将要研究的理论范畴。其目的是了解禁闭和手征对称破缺，这两个特征有助于理解质量生成和这些理论的大部分低能非微扰方面。我们将考虑SU(N)规范群，并考虑大量颜色(N)的限制。我们将规范理论耦合到伴随表象中的夸克。利用一种称为约化的现象，我们将能够在单格点格子上数值研究该理论，其中夸克味道的数量被扩展到具有任何实际值。这将使我们能够研究共形和近共形理论，并帮助我们理解质量生成。QCD中的去禁闭跃迁目前正在进行密集的实验研究，我们将研究重子化学势在QCD大N极限中的作用。二维费米子将被用来研究类QCD理论大N极限中的强耦合到弱耦合跃迁。我们将研究多偏好QCD中夸克质量的影响，特别是考虑负夸克质量的情况，目的是在质量参数空间中确定一条曲线，其中一个人有无质量的介子。夸克携带有色电荷，核物质是由胶子介导的有色夸克的结合形成的。量子色动力学(QCD)是描述这些颜色电荷相互作用的理论。实验表明，夸克有三种颜色，但所有的核物质都是中性的。无质量的夸克和胶子产生有质量的核物质。理解这种大质量的产生是至关重要的，这个项目将通过关注限制大量颜色的类QCD理论来解决这个问题的各种方法。这样的理论与弦理论的最新发展密切相关，我们将能够在场论和弦理论之间建立联系。科学方法包括分析计算和数值计算。在最近的研究生工作中具有这方面经验的博士后研究员将由私人投资指导开展提案的几个方面的工作。计算机集群将用于数值计算，作为这一提议的一部分而获得的结果将在核物理和粒子物理的国际会议上公布。

Numerical studies of non-abelian gauge theories coupled to fermions in different representations of the gauge group will form the central focus of all projects in this proposal. Quantum chromodynamics (QCD) belongs to the class of theories we will investigate. The aim is to understand confinement and chiral symmetry breaking, the two features that help understand mass generation and much of the low energy non-perturbative aspects of these theories. We will consider the SU(N) gauge group and consider the limit of a large number of colors (N). We will couple the gauge theory to quarks in the adjoint representation. Using a phenomenon called reduction, we will be able to numerically study the theory on a single site lattice with the number of quark flavors extended to take on any real value. This will enable us to study conformal and near-conformal theories and help us understand mass generation. The de-confinement transition in QCD is currently under intense experimental investigation and we will study the role of baryonic chemical potential in the large-N limit of QCD. Two-dimensional fermion will be used as a probe to study the strong to weak coupling transition in the large N limit of QCD-like theories. We will study the effect of quark masses in multi-favor QCD and, in particular, consider the case of negative quark masses with the aim of identifying a curve in the space of mass parameters where one has massless pions. Quarks carry a color charge and nuclear matter is formed from the binding of colored quarks mediated by gluons. Quantum chromodynamics (QCD) is the theory that describes the interaction of these color charges. Experiments have shown that quarks come in three colors but all nuclear matter is color neutral. Massless quarks and gluons give rise to nuclear matter that has mass. An understanding of this mass generation is of fundamental importance and this project will address various approaches to this problem by focusing on QCD-like theories in the limit of large number of colors. Such theories are closely related to recent developments in string theory and we will be able to make connections between field theory and string theory. The scientific methods involve analytical calculations and numerical computations. A post-doctoral fellow with prior experience in this area during his/her recent graduate work will be mentored by the PI to work on several aspects of the proposal. Computer clusters will be used for numerical computations and the results obtained as part of this proposal will be presented at international conferences in nuclear and particle physics.