# New Ideas in Gauge, String and Lattice Theory (Transfer)

Lead Research Organisation:
University of Liverpool

Department Name: Mathematical Sciences

### Abstract

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 scale probed 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.

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 scale probed 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.

### Planned Impact

Knowledge Exchange is centred on the exploitation of HPC facilities, especially through the close involvement of the UKQCD collaboration with IBM and the development of the Blue Gene series of supercomputers. The Swansea group has established a close contact with IBM Research at Yorktown Heights, running lattice code as a benchmark application to evaluate computer performance and development. This has led to the creation of a third-party company, BSMBench Ltd, to commercialise a benchmarking tool developed from the group's research in lattice gauge theory. Through UKQCD, both groups are active in developing Grid technology.

Outreach activities are focused in three areas - schools activities, popular lectures and media involvement. The Swansea group organises two activities for schools: Particle Physics Masterclasses for 6th form students with lectures and hands-on computer sessions using ATLAS software to analyse LHC events, and annual Christmas lectures for younger pupils. Group members give frequent public lectures and organise the local Swansea `Science Cafe'. The excitement surrounding the first experimental results and discovery of the Higgs boson at CERN, as well as the achievement of the Physics Department's atomic physics group in creating and trapping atoms of antihydrogen at CERN, have been exploited in numerous TV and radio presentations as well as in newspaper and magazine articles. The keynote lecture by Peter Higgs at the `Strong and Electroweak Matter' conference in Swansea in July 2012 was streamed to schools across the U.K. and an interview with Peter was posted on the University's website and You Tube.

Outreach activities are focused in three areas - schools activities, popular lectures and media involvement. The Swansea group organises two activities for schools: Particle Physics Masterclasses for 6th form students with lectures and hands-on computer sessions using ATLAS software to analyse LHC events, and annual Christmas lectures for younger pupils. Group members give frequent public lectures and organise the local Swansea `Science Cafe'. The excitement surrounding the first experimental results and discovery of the Higgs boson at CERN, as well as the achievement of the Physics Department's atomic physics group in creating and trapping atoms of antihydrogen at CERN, have been exploited in numerous TV and radio presentations as well as in newspaper and magazine articles. The keynote lecture by Peter Higgs at the `Strong and Electroweak Matter' conference in Swansea in July 2012 was streamed to schools across the U.K. and an interview with Peter was posted on the University's website and You Tube.

### Publications

Langfeld K
(2016)

*From the Density-of-states Method to Finite Density Quantum Field Theory*in Acta Physica Polonica B Proceedings Supplement
Garron N
(2017)

*Controlling the sign problem in finite-density quantum field theory*in The European Physical Journal C
Garron N
(2016)

*Anatomy of the sign-problem in heavy-dense QCD*in The European Physical Journal C
Langfeld K
(2017)

*Density of states*Description | The density-of-states approach is a novel numerical method that, during the grant period, was applied to computer simulations of dense quantum matter. These simulations would provide rare first principle insight into the properties of elusive matter such as in compact stars or Graphene if it were not for the notorious sign problem, which has hampered these simulations for more than 3 decades. Our new approach mitigates the sign problem, and we could show for QCD (the theory of string interactions) with heavy quarks that important exact results (within statistical errors) can be expected for the realistic case. We are also now confident that the method will reveal important new information about new materials such as Graphene. |

Exploitation Route | The new numerical method resonates with scientists working in Bayesian Statistics and Rare Event simulations. I am in contact to define a company driven PhD student project with the newly created, EPSRC funded Centre for Doctoral Training (CDT) "Distributed Algorithms" in Liverpool. |

Sectors | Aerospace, Defence and Marine,Financial Services, and Management Consultancy |

URL | https://www2.physik.uni-bielefeld.de/fileadmin/user_upload/Sign18/langfeld_sign3.pdf |

Description | It has turned out that the density-of-states approach can aide the field of "Rare Event Simualtions". This is currently explored in part in the EPSRC project "Big Hypotheses: A Fully Parallelised Bayesian Inference Solution". Although direct Impact has not yet materialised, it is expected that this might be the case at a three year time scale. |

First Year Of Impact | 2019 |

Sector | Aerospace, Defence and Marine,Financial Services, and Management Consultancy |

Impact Types | Societal,Economic |