New Frontiers of Lattice Field Theory

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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.