New Ideas in Gauge, String and Lattice Theory

粒子物理学的标准模型将我们目前对原子基本成分和物质本质的认识编码为宇宙大爆炸后最早的时刻。然而，我们对标准模型动力学的理解受到我们解决其强相互作用领域的能力的限制，量子色动力学（QCD）描述了夸克和胶子的相互作用。斯旺西和普利茅斯的研究小组正从两个互补的角度来研究这个问题。通过将时空的连续体近似为点的离散晶格，可以在高性能计算机上模拟QCD。这些小组将在高温和高密度的极端条件下研究晶格QCD，这些条件存在于大爆炸之后，现在可以在欧洲核子研究中心的大型强子对撞机（LHC）的重离子碰撞中实现。这些研究将由“量规-重力二象性”所产生的分析见解加以补充，“量规-重力二象性”是一个了不起的原理，它将描述粒子物理的理论与广义相对论的性质联系起来。然而，大型强子对撞机的主要目标是发现产生基本粒子质量的新物理原理。这种“电弱对称性破缺”是标准模型中最难以理解的部分。这可能是由于穿越时空的背景场的存在，当粒子与背景场相互作用时，背景场赋予了粒子质量。另一方面，大质量的产生可能是由于在大型强子对撞机探测到的TeV能量尺度上存在一种新的强相互作用。在这两种情况下，理论都预测了一种新的自旋零粒子的存在，即最近在大型强子对撞机中发现的著名的希格斯玻色子。区分这些可能性是一个微妙的问题，我们再次尝试使用量规重力对偶性和晶格模拟来解决这个问题。然而，粒子物理学家并不认为标准模型是自然界的终极理论。它是规范理论的一个例子，规范理论是一个理论框架，它将量子力学和狭义相对论以及物理学家通过几十年的粒子加速器实验发现的基本对称性统一起来。与此同时，引力仍然在这个框架之外，被广义相对论用时空曲率来描述。更深层次的统一可能出现超弦,同时包含测量理论和引力与一种新型的时空对称性称为超对称性。因此，斯旺西的研究小组在对大型强子对撞机物理学的研究之外，还对规范场和弦的更深层次结构进行了研究，利用规范引力对偶性和“量子可积性”等基本思想来寻找我们当前粒子物理理论背后的基本原理。

The standard model of particle physics encodes our current knowledge of the fundamental constituents of atoms and the nature of matter in the earliest moments following the Big Bang. However, our understanding of the dynamics of the standard model is limited by our ability to solve its strongly-interacting sector, quantum chromodynamics (QCD), which describes the interactions of quarks and gluons. The Swansea and Plymouth groups are approaching this problem from two complementary perspectives. By approximating the continuum of spacetime as a discrete lattice of points, it is possible to simulate QCD on high performance computers. The groups will study lattice QCD in the extreme conditions of high temperature and density which existed following the Big Bang and which can now be realised in heavy-ion collisions at the Large Hadron Collider (LHC) at CERN. These investigations will be complemented by analytic insights arising from `gauge-gravity duality', a remarkable principle which relates the theories describing particle physics with properties of general relativity. The primary goal of the LHC is, however, to discover the new physics which is responsible for the generation of mass for the elementary particles. This `electroweak symmetry breaking' is the least understood part of the standard model. It may be due to the existence of a background field permeating spacetime, which gives mass to particles as they interact with it. On the other hand, mass generation may be due to the existence of a new strong interaction at the TeV energy scaleprobed by the LHC. In both cases, the theories predict the existence of a new spin zero particle, the famous Higgs boson recently discovered at the LHC. Distinguishing these possibilities is a subtle problem and once again we are attempting to resolve the question using both gauge-gravity duality and lattice simulations. Particle physicists do not, however, believe that the standard model is the ultimate theory of nature. It is an example of a gauge theory, a theoretical framework which unifies quantum mechanics and special relativity together with the fundamental symmetries which physicists have discovered through decades of experiments with particle accelerators. Meanwhile, gravity remains outside this framework, being described by general relativity in terms of the curvature of spacetime. A deeper unification appears possible with superstrings, which contain both gauge theories and gravity together with a new type of spacetime symmetry known as supersymmetry. The Swansea group is therefore complementing its investigations of LHC physics with research into the deeper structure of gauge fields and strings, using fundamental ideas such as gauge-gravity duality and `quantum integrability' in the search for the underlying principles behind our current theories of particle physics.