# New Ideas in Gauge, String and Lattice Theory

Lead Research Organisation:
Swansea University

Department Name: College of Science

### 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

The Pathways to Impact document summarises the activities of the Plymouth and Swansea groups in the areas of Knowledge Exchange and Outreach.

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.

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.

### Publications

Bennett E
(2020)

*S p ( 4 ) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions*in Physical Review D
Bartolo N
(2016)

*Science with the space-based interferometer LISA. IV: probing inflation with gravitational waves*in Journal of Cosmology and Astroparticle Physics
Hansen M
(2018)

*Simulations of QCD and QED with C * boundary conditions*in EPJ Web of Conferences
Appelquist T
(2016)

*Spectrum-doubled heavy vector bosons at the LHC*in Journal of High Energy Physics
Chagoya J
(2018)

*Stealth configurations in vector-tensor theories of gravity*in Journal of Cosmology and Astroparticle Physics
Armour W
(2015)

*Strong interaction effects at a Fermi surface in a model for voltage-biased bilayer graphene*in Physical Review B
Parameswaran S
(2016)

*Subleading effects and the field range in axion inflation*in Journal of Cosmology and Astroparticle Physics
Faedo A
(2014)

*Supersymmetric Lifshitz-like backgrounds from $ \mathcal{N} $ = 4 SYM with heavy quark density*in Journal of High Energy Physics
Lee J
(2017)

*Symmetry restoration at high-temperature in two-color and two-flavor lattice gauge theories*in Journal of High Energy Physics
Magnifico G
(2019)

*Symmetry-protected topological phases in lattice gauge theories: Topological QED 2*in Physical Review D
Hollowood T
(2014)

*Symplectic deformations of integrable field theories and AdS/CFT*in Physics Letters B
Aarts Gert
(2014)

*Systematic approximation for QCD at non-zero density*in PoS
Itsios G
(2017)

*The AdS 5 non-Abelian T-dual of Klebanov-Witten as a N = 1 $$ \mathcal{N}=1 $$ linear quiver from M5-branes*in Journal of High Energy Physics
Allton Chris
(2015)

*The Charmonium Potential at Non-Zero Temperature*
Langfeld K
(2015)

*The density of states approach for the simulation of finite density quantum field theories*in Journal of Physics: Conference Series
Hollowood T
(2014)

*The emergent Copenhagen interpretation of quantum mechanics*in Journal of Physics A: Mathematical and Theoretical
Aarts G
(2015)

*The Phase Diagram of Heavy Dense QCD with Complex Langevin Simulations*in Acta Physica Polonica B Proceedings Supplement
Armoni A
(2015)

*The quark condensate in multi-flavour QCD - planar equivalence confronting lattice simulations*in Physics Letters B
Amato Alessandro
(2015)

*Topology and glueballs in $SU(7)$ Yang-Mills with open boundary conditions*in PoS
Langfeld Kurt
(2013)

*Towards a density of states approach for dense matter systems*in PoS
Aarts Gert
(2015)

*Towards the heavy dense QCD phase diagram using Complex Langevin simulations*in PoS*Towards the heavy dense QCD phase diagram using Complex Langevin simulations*in PoS

Amato Alessandro
(2013)

*Transport coefficients of the QGP*in PoS
Boz T
(2016)

*Two-color QCD at high density*
Dunbar D
(2016)

*Two-loop five-point all-plus helicity Yang-Mills amplitude*in Physical Review D
Dunbar D
(2017)

*Two-loop gravity amplitudes from four dimensional unitarity*in Physical Review D
Dunbar D
(2016)

*Two-loop n -point all-plus helicity amplitude*in Physical Review D
Dunbar DC
(2016)

*Two-Loop Six Gluon All-Plus Helicity Amplitude.*in Physical review letters
Macpherson Niall T.
(2014)

*Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and Non-Abelian T Dualities*
Macpherson N
(2015)

*Type IIB supergravity solutions with AdS5 from Abelian and non-Abelian T dualities*in Journal of High Energy Physics
McDonald J
(2016)

*WITHDRAWN: Leptogenesis and gravity: Baryon asymmetry without decays*in Physics Letters B
Appadu C
(2017)

*Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices*in Journal of High Energy PhysicsDescription | The research group has made significant progress on all the topics proposed in the "New Ideas in Gauge, String and Lattice Theory" grant, with almost 200 papers being published in the grant period. A selection of highlights include: Quantum Field Theory and Gravity: A new mechanism - 'radiatively induced gravitational leptogenesis' - was developed to explain the matter-antimatter asymmetry of the universe, exploiting subtle features of gravitational interactions with the quantum self-energy cloud of the light neutrinos. Holography: Non-abelian T duality in holographic theories was shown to generate new solutions of string and M-theory exhibiting novel physical (Wilson loop, symmetry breaking, central charges) and geometric (AdS factors, G structures) features. Holographic conformal field theory was used to calculate the thermodynamic and entanglement entropies of conformal field theories with higher spin charges. Integrability: It was shown that the AdS5 x S5 string theory admits an integrable deformation for which the worldsheet theory is a WZW model based on a subgroup, extending previous analyses of the S-matrix in these theories. Amplitudes: The development of improved unitarity and augmented recursion techniques allowed the calculation of a range of new one and two-loop amplitudes including the 1-loop, 6-point NMHV amplitude in N=4 supergravity and the 2-loop, 6 gluon all-plus helicity amplitude in QCD. Beyond the Standard Model: The existence of a light Higgs-like scalar particle, a pseudo-dilaton, has been revealed and studied in a class of holographic BSM models. Seiberg duality was extended to non-supersymmetric gauge theories, allowing an analytic non-perturbative investigation of strong-coupling phenomena including the range of the conformal window. Hot and Dense Lattice: The FASTSUM lattice collaboration (supported also by grants from DIRAC, PRACE and Hartree HPC) has demonstrated the melting properties of different heavy-quarkonium states across the deconfinement phase transition in QCD at high temperature, results of importance to the LHC heavy-ion programme. Improved, detailed studies were made of the spectral functions determining transport coefficients in QCD, with new results for the electrical conductivity and charge diffusion coefficient consistent with expectations from holographic models. The first applications to QCD at non-zero baryon density were made using the complex Langevin approach to the 'sign problem'. BSM Lattice: It was demonstrated through lattice investigations of SU(2) gauge theories with Dirac adjoint quarks that near-conformal gauge theories can exhibit large anomalous dimensions, a potentially key ingredient for realistic strong-coupling BSM models of electroweak symmetry breaking. |

Exploitation Route | This research is an integral part of the ongoing UK and international activity in particle theory. The topics addressed and resolved will inform the work of particle theorists working across a spectrum from fundamental mathematical theory to LHC phenomenology. |

Sectors | Digital/Communication/Information Technologies (including Software),Education |

Description | Knowledge Exchange: Activities covered by the STFC Consolidated grant are closely linked to the formation and execution of Supercomputing Wales, the successor to HPC Wales. Biagio Lucini is Swansea PI of Supercomputing Wales and the lattice QCD group is one of main users of the facility, leveraged by the STFC Consolidated grant as a target towards grant income required by WEFO. On a related basis, Swansea University has recently founded its Swansea Academy for Advanced Computing. SA2C has been set up to further the university research objectives by providing state of the art research computing technology and skills to researchers at Swansea University. With Biagio Lucini as Director, SA2C currently employs 5 research software engineers, three of which are (former) lattice gauge theorists. Public Outreach: Oriel Science is a public outreach project developed under the leadership of Prof Chris Allton. It has established a city-centre location in Swansea and hosts exhibitions based on science research in the University, as well as coordinating an extensive schools science outreach programme. An exhibition "The Story of Time" in 2016 highlighted our STFC funded research on the LHC and quantum aspects of gravity. Prof Allton has since been awarded an STFC Leadership Fellowship in Public Engagement to build on his work as Director of Oriel Science, and the project is supported by a Public Engagement Spark Award. |

First Year Of Impact | 2016 |

Sector | Digital/Communication/Information Technologies (including Software),Education,Culture, Heritage, Museums and Collections |

Impact Types | Economic |

Description | Leverhulme Fellowship |

Amount | £45,000 (GBP) |

Funding ID | LT140052 |

Organisation | The Leverhulme Trust |

Sector | Charity/Non Profit |

Country | United Kingdom |

Start | 10/2015 |

End | 09/2016 |

Description | UKQCD |

Organisation | UKQCD |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | The Swansea Lattice Gauge Theory research group is a member of the UKQCD lattice consortium. |

Collaborator Contribution | Collaboration on physics content of research papers and use of HPC facilities. |

Impact | 30 of the refereed publications listed here (authors Aarts, Allton, Hands, Lucini) are in teh field of Lattice Gauge Theory and are related to some extent with UKQCD. The Swansea share of UKQCD's STFC HPC equipment grant procured a £1.2M IBM Blue Gene/P computer located in Swansea. The relation with IBM and software development formed part of the Department's submission in the 2010 REF Impact Pilot exercise. |

Description | Oriel Science Exhibition Centre |

Form Of Engagement Activity | Participation in an activity, workshop or similar |

Part Of Official Scheme? | No |

Geographic Reach | Regional |

Primary Audience | Public/other audiences |

Results and Impact | Prof Chris Allton has led the creation of an Exhibition Centre, named "Oriel Science", in Swansea city centre, presenting the research activity of the University's College of Science to the general public and school visits. The exhibition on "The Story of Time" highlighted research related to the particle theory group's STFC consolidated grant. |

Year(s) Of Engagement Activity | 2016,2017 |

URL | http://www.orielscience.co.uk |

Description | Particle Physics Masterclasses |

Form Of Engagement Activity | Participation in an open day or visit at my research institution |

Part Of Official Scheme? | Yes |

Geographic Reach | Regional |

Primary Audience | Schools |

Results and Impact | Approx 120 pupils annually attend two or three separate day-long events featuring lectures and hands-on computer exercises featuring CERN, the LHC, particle physics, ATLAS software and the ALPHA antihydrogen collaboration. Around 10 schools attend each year. Most have asked to be re-invited on a regular basis to future year's events. |

Year(s) Of Engagement Activity | 2015 |

Description | Radio Interviews |

Form Of Engagement Activity | A press release, press conference or response to a media enquiry/interview |

Part Of Official Scheme? | No |

Geographic Reach | National |

Primary Audience | Public/other audiences |

Results and Impact | Interviews and participation on science programmes for BBC Radio Wales, including Science Cafe programmes on string theory, particle physics and cosmology, the anniversary of Hawking's "Brief History of Time" and the Centenary of Einstein's General Relativity. Not possible to quantify. |

Year(s) Of Engagement Activity | 2015 |