标题： 强相互作用量子场论中的共形行为研究 显示英文标题

标题： Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories

摘要： 在本论文中，我们展示了利用数值和分析技术相结合的方法，非微扰地表征各种共形和近似共形量子场理论的工作。 一个关键的研究领域是四维规范理论的共形窗口，该理论带有狄拉克费米子，并且可能适用于标准模型之外的物理。 在第一章中，我们回顾了一些关于复合 希格斯场景模型的历史，以激励对接近共形窗口的规范理论的研究。 在第二章中，我们回顾了特定理论的格点研究，即具有八种狄拉克费米子的SU(3)规范理论，这些费米子处于规范群的基本表示中。 我们特别关注这一模型光谱中出现的轻夸克单态标量状态及其作为复合希格斯玻色子的可能作用。 我们提倡一种表征近似共形规范理论的方法，其中格点计算被用来识别这些近似共形规范理论的最佳低能有效场论（EFT）描述，然后将格点方法和EFT作为互补工具来分类这些理论中的低能物理的一般特征。 我们展示了使用Lüscher有限体积方法在格点上计算的最大同位旋 $\pi\pi \rightarrow \pi\pi$ 散射的新结果。 这项散射研究旨在为进一步约束近似共形规范理论的可能EFT描述提供更多的数据。 在第三章中，我们回顾了手征有效理论从当前代数方法到手征拉格朗日和现代有效场论技术的历史发展。 我们提出了一种基于线性sigma模型的新EFT框架，用于描述近似共形规范理论的低能状态。 我们... (摘要全文在此内) 显示英文摘要

摘要： In this dissertation, we present work towards characterizing various conformal and nearly conformal quantum field theories nonperturbatively using a combination of numerical and analytical techniques. A key area of interest is the conformal window of four dimensional gauge theories with Dirac fermions and its potential applicability to beyond the standard model physics. In the first chapter, we review some of the history of models of composite Higgs scenarios in order to motivate the study of gauge theories near the conformal window. In the second chapter we review lattice studies of a specific theory, SU(3) gauge theory with eight flavors of Dirac fermions in the fundamental representation of the gauge group. We place a particular emphasis on the light flavor-singlet scalar state appearing in the spectrum of this model and its possible role as a composite Higgs boson. We advocate an approach to characterizing nearly conformal gauge theories in which lattice calculations are used to identify the best low energy effective field theory (EFT) description of such nearly conformal gauge theories, and the lattice and EFT are then used as complementary tools to classify the generic features of the low energy physics in these theories. We present new results for maximal isospin $\pi\pi \rightarrow \pi\pi$ scattering on the lattice computed using L\"uscher's finite volume method. This scattering study is intended to provide further data for constraining the possible EFT descriptions of nearly conformal gauge theory. In Chapter 3, we review the historical development of chiral effective theory from current algebra methods up through the chiral Lagrangian and modern effective field theory techniques. We present a new EFT framework based on the linear sigma model for describing the low lying states of nearly conformal gauge theories. We place a ... (full abstract within)