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These pages provide non-technical (or at least less-technical) descriptions of my research projects, intended for interested non-experts. I write them both to contribute to public engagement with science and to recognize taxpayer support of my work over the years. Experts may prefer this more technical summary. If you have any questions about my work, or comments on this attempt to present it as comprehensibly and correctly as I can, you are welcome to contact me.

The essence of my research is to use high-performance computing to gain insight into strongly interacting quantum field theories, through a framework known as lattice gauge theory. This page provides some background on strong dynamics and lattice gauge theory. Below I summarize various projects I've carried out over the years, each of which has its own page providing further information (currently being updated throughout June 2018). For each project I also link my related publications, all of which are freely available online, mostly through the arXiv e-print server.

It is important to note that all of this work involves various forms of collaboration, reflected in part by the authorship of those publications. These pages reflect my own views and interests, and I am solely responsible for any errors or omissions.

Supersymmetric lattice field theories

Supersymmetry image While supersymmetry is most famous as a possible extension of the standard model of particle physics, at a more fundamental level it simplifies the systems in question, allowing profound insights into strongly coupled dynamics. These include, for example, the concept of holographic duality between field theories and higher-dimensional gravity. Lattice calculations provide a unique means to analyse supersymmetric field theories from first principles, enabling new tests of such dualities as well as potential new discoveries. Full discussion.

Related publications: arXiv:1710.06398, arXiv:1709.07025, arXiv:1611.06561, Lat16:209, arXiv:1512.01137, arXiv:1508.00884, arXiv:1505.03135, arXiv:1411.0166, arXiv:1410.6971, arXiv:1405.0644

Composite Higgs physics and electroweak phenomenology

Composite Higgs image The Higgs boson discovered in 2012 may be a composite particle arising from new strong dynamics beyond the standard model, which would explain how it is protected against large quantum corrections. This possibility is currently being investigated by experiments at the Large Hadron Collider, which are imposing increasingly tight phenomenological constraints on composite Higgs models. Using lattice gauge theory I am obtaining first-principles predictions for the behavior of representative new strong dynamics potentially underlying such models, to be compared against experimental results. Full discussion.

Related publications: arXiv:1601.04027, arXiv:1405.4752, arXiv:1310.7006, arXiv:1309.1206, arXiv:1201.3977, arXiv:1111.4993, PhD dissertation, arXiv:1009.5967, arXiv:1002.3777, arXiv:0910.2224

Conformal and near-conformal strong dynamics

Conformality image The investigations of composite Higgs physics discussed above find that agreement with experimental results improves for theories whose dynamics evolve slowly across a wide range of length scales. This "near-conformal" dynamics is difficult to study through numerical lattice calculations, since only a limited range of length scales can be explored in computations that are practical to run using existing and foreseeable computing hardware. This motivated significant effort to develop and apply improved lattice techniques to study near-conformal field theories. Full discussion.

Related publications: arXiv:1610.10004, arXiv:1506.08791, arXiv:1410.5886, arXiv:1404.0984, arXiv:1401.0195, arXiv:1311.4889, arXiv:1311.2679, arXiv:1311.1287, arXiv:1310.1124, arXiv:1309.1206, arXiv:1303.7129, arXiv:1301.1355, arXiv:1212.0053, arXiv:1207.7164, arXiv:1207.7162, arXiv:1204.6000, arXiv:1111.2317, arXiv:1106.2148

Quantum chromodynamics at non-zero baryon density

Finite density image A long-standing challenge for lattice gauge theory is the analysis of systems with many more particles than anti-particles. For example, in neutron stars there is a high density of baryons (protons and neutrons) with relatively few anti-baryons. In lattice calculations that use standard importance sampling algorithms this leads to the appearance of nonsensical negative probabilities, which is known as a sign problem. I recently began exploring novel algorithmic approaches designed to reduce the severity of sign problems in lattice calculations. Full discussion.

Related publication: arXiv:1712.07585

Composite dark matter

Dark matter image It is a remarkable possibility that the dark matter discovered by many different observations of the large-scale universe could consist of composite particles that contain electrically charged constituents. These constituents interact with light but the composite particles they produce are dark, much like electrically charged quarks produce the electrically neutral neutron. Lattice calculations have provided predictions for how such composite dark matter may be seen in ongoing experiments using large underground detectors. Work is in progress to predict additional observable signatures of composite dark matter at high-energy particle colliders and future gravitational wave observatories. Full discussion.

Related publications: arXiv:1503.04205, arXiv:1503.04203, arXiv:1402.6656, arXiv:1301.1693

Topological phases and topological phase transitions

Four-fermion image Phase transitions typically separate a phase with a broken symmetry from a different phase in which that symmetry is preserved, allowing the phases to be distinguished by a local order parameter. More recently transitions have been discovered between distinct phases with the same symmetries, which are instead distinguished by non-local "topological" properties. The importance of these topological phase transitions was recognized by the 2016 Nobel Prize in Physics. My work in this area investigates simple lattice field theories that may exhibit topological phase transitions, in particular considering a mechanism to generate particle masses without breaking any symmetries. Full discussion.

Related publications: arXiv:1710.08137, arXiv:1609.08541

Strange quark content of the nucleon

Strangeness image Quantum fluctuations in the strange-quark field affect the properties of composite particles even when the quantum numbers of those composite particles don't depend on strange quarks. This is the case for nucleons (protons and neutrons), where the strange-quark contribution to the mass of the nucleon play a role in searches for dark matter in large underground detectors. I have used lattice QCD to investigate strange-quark contributions both to the mass and to the internal structure of nucleons, which requires challenging computations of quark-line-disconnected diagrams. Full discussion.

Related publications: Lat12:166, arXiv:1012.0562


Graphene image The 2010 Nobel Prize in Physics was awarded to recognize the experimental isolation and characterization of graphene, a remarkable two-dimensional material consisting of carbon atoms arranged in a regular honeycomb lattice. Among the many unusual properties of graphene, in the context of lattice field theory the existence of strongly interacting massless fermion quasi-particles is particularly significant. My work on graphene focused on showing how lattice gauge theory can be applied to study this material non-perturbatively from first principles. Full discussion.

Related publications: arXiv:1204.5424, arXiv:1101.5131

Algorithm development

Algorithms image Full discussion.

Related publications: arXiv:1403.2761, arXiv:0906.2813, arXiv:0902.0045, Bachelor thesis

Last modified 21 June 2018

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