New Frontiers of Lattice Field Theory

宇宙的基本组成和结构是什么，它们是如何相互作用的？我的研究使用格点场论的计算框架来解决这些问题。这种方法用离散时空点的有限网格代替空间和时间，简化了预测物理现象所需的复杂计算。通过使用高性能超级计算来分析越来越多的点越来越靠近的晶格，我们可以预测我们所生活的连续空间和时间。晶格场论最著名的研究是产生复合粒子（如质子和中子）的强核力。该项目将把这项技术应用于三个新的前沿领域，以应对关键的科学挑战，并推进我们对宇宙的理解。第一个前沿领域是调查希格斯玻色子或宇宙中的暗物质是否可能是复合粒子，在某些方面类似于中子。这种可能性可以解释这些粒子目前神秘的方面。我的格点场论计算所产生的预测将通过正在进行的和未来的实验进行测试，包括欧洲核子研究中心的大型强子对撞机。此外，我还将预测复合暗物质可能产生的引力波的特征，这是未来引力波观测站将寻找的。第二个前沿领域涉及超对称性的研究，这是对自然定律的一种假设性扩展。晶格超对称性的一个特别重要的目标是测试所谓的全息二元性，它推测这些超对称系统秘密地描述了量子引力弦理论的行为。我将通过计算超对称的热力学来验证这一点，全息对偶性声称超对称应该与弦论中黑洞的行为相匹配，最后我将讨论一个被称为符号问题的问题，这个问题目前阻碍了从中子星到超导体的许多不同物理系统的晶格研究。当数值网格计算所使用的算法遇到负数时，就会出现符号问题，因为它们期望概率在0%到100%之间。除了开发和测试可能解决某些系统中的符号问题的新算法外，我还将量子计算作为一种特别新颖的方法来解决符号问题。量子计算是一项潜在的革命性新兴技术，其动机是，由于它采用的量子方法，自然界没有任何困难实现许多物理系统。这些基本粒子的研究，它们的相互作用，以及它们与量子引力的全息联系对科学家和公众都很有吸引力。与大型强子对撞机和引力波观测站的实验的相互作用增加了兴奋，先进计算，算法突破和量子计算的关键新兴技术的作用也是如此。

What are the fundamental constituents and fabric of the Universe and how do they interact? My research addresses these questions using the computational framework of lattice field theory. This approach replaces space and time by a finite lattice of discrete space-time points, simplifying the complicated calculations needed to predict physical phenomena. By using high-performance supercomputing to analyse lattices with more and more points closer and closer together, we obtain predictions for the continuous space and time in which we live.Lattice field theory is best known for studies of the strong nuclear force that produces composite particles such as the proton and neutron. This project will apply the technique to three new frontiers, to address key scientific challenges and advance our understanding of the Universe.The first frontier is to investigate whether the Higgs boson or the dark matter of the Universe may be composite particles, similar in certain ways to the neutron. This possibility could explain currently mysterious aspects of these particles. The predictions produced by my lattice field theory calculations will be tested by ongoing and future experiments including those at CERN's Large Hadron Collider. In addition, I will predict features of the gravitational waves that may be produced by composite dark matter, which future gravitational wave observatories will search for.The second frontier involves investigations of supersymmetry, a hypothetical extension to the laws of Nature. A particularly important target for lattice supersymmetry is to test so-called holographic duality, which conjectures that these supersymmetric systems secretly describe the behaviour of string theories of quantum gravity. I will test this by computing the thermodynamics of supersymmetry, which holographic duality claims should match the behaviour of black holes in string theory.Finally I will address an issue known as the sign problem, which currently obstructs lattice investigations of many different physical systems from neutron stars to superconductors. The sign problem arises when the algorithms used by numerical lattice computations encounter negative numbers where they expect probabilities (between 0% and 100%). In addition to developing and testing new algorithms that may solve the sign problem in certain systems, I will also apply quantum computing as a particularly novel approach to the sign problem. Quantum computing is a potentially revolutionary emerging technology, motivated by the fact that Nature does not have any difficulty realising many of the physical systems in question thanks to the quantum methods that it employs.These investigations of elementary particles, their interactions, and their holographic connections to quantum gravity are fascinating both for scientists and the general public. The interplay with experiments at the Large Hadron Collider and gravitational wave observatories adds to the excitement, as does the role of advanced computing, algorithmic breakthroughs and the key emerging technology of quantum computing.