标题： 非微扰研究非共形场理论 显示英文标题

标题： Non-perturbative Studies of Non-conformal Field Theories

摘要： 标准模型中许多令人兴奋的特性本质上是非微扰的。 对超出基本粒子标准模型的许多物理方面的理论理解也需要一个非微扰框架。 一种这样的框架涉及在时空格点上离散化量子场论。 我们可以使用这种格点正则化方法来研究超出标准模型的超对称版本的物理。 在本论文中，我们讨论了时空格点设置，并通过不同模型的例子，我们将看到该工具在探索无法通过微扰理论访问的场论区域中的数值能力。 我们使用一种高效的蒙特卡洛算法来更新路径积分中的场配置，最终达到平衡配置。 一种规范/引力假设的版本将弱耦合的引力理论与强耦合的场论联系起来。 我们将主要关注较低维中假设的非共形类似物。 本论文主要讨论两个低维模型的数值模拟结果。 一个是BMN矩阵量子力学的玻色版本，另一个是包含四个超对称性的二维杨-米尔斯理论。 我们的数值结果表明，玻色BMN模型的相图在所有耦合下平滑地在玻色BFSS模型和规范高斯模型之间过渡，并且存在一阶禁闭相变。 我们对包含四个超对称性的二维杨-米尔斯理论的模拟结果表明，该模型在颜色数大的极限下允许禁闭相变。 我们还表明，在弱耦合区域，该转变的性质与其最大超对称亲戚相似。 显示英文摘要

摘要： Many of the exciting features of the Standard Model of the elementary particles are inherently non-perturbative. A theoretical understanding of many physics aspects beyond the Standard Model of elementary particles also requires a non-perturbative framework. One such framework involves discretizing quantum field theories on a spacetime lattice. We can use this lattice regularization method to study supersymmetric versions of physics beyond the Standard Model. In this thesis, we discuss the spacetime lattice setup, and with the examples of different models, we will see the numerical capability of this tool in exploring field theory regimes that are not accessible through perturbation theory. We use an efficient version of the Monte Carlo algorithm to update the field configurations in the path integral and eventually reach the equilibrium configurations. A version of the gauge/gravity conjecture connects weakly coupled gravitational theories to strongly coupled field theories. We will mainly focus on the non-conformal analogs of the conjecture in lower dimensions. This thesis mainly discusses the numerical simulation results of two lower-dimensional models. One is the bosonic version of the BMN matrix quantum mechanics and the other is a two-dimensional Yang-Mills theory containing four supersymmetries. Our numerical results suggest that the phase diagram of bosonic BMN model smoothly interpolates between the bosonic BFSS and the gauged Gaussian model, with first-order deconfinement phase transition at all couplings. Our simulation results for two-dimensional Yang-Mills theory that contains four supersymmetries show that this model admits a deconfinement phase transition in the limit of a large number of colors. We also show that the nature of the transition looks similar to its maximally supersymmetric cousin in the weak coupling regime.