# Particles, Fields and Spacetime

Lead Research Organisation:
Durham University

Department Name: Mathematical Sciences

### Abstract

All matter in the universe and the fundamental forces apart from gravity appear to be well described by particle theories, in which the fundamental components of matter are pointlike particles, which interact by exchanging other kinds of particles. Quantum field theory is the mathematical language describing these particle theories; the particles describing forces are described by a class of theories called gauge theories. However, it appears we need to go beyond quantum field theory to include gravity. The leading candidate for this extension is string theory, which is based on the idea that the particles are actually one-dimensional loops of string, with the interactions described by smooth surfaces connecting different strings.

One strand of our research is the development of new tools for computations in quantum field theory. In one line of research, it has been understood that certain gauge theories have additional previously unsuspected symmetries, which explain the mysterious simplicity of some computational results. This has been developed to obtain more efficient calculational techniques for increasingly general questions. In an independent line, a symmetry called conformal symmetry has been newly exploited to constrain the particle content and interactions of theories with this symmetry. We aim to develop these tools further and bring them together with the long-term goal of completely solving the simplest, most symmetric theories. We also have a broad programme of research on aspects of field theory far from the vacuum, including work on smooth classical solutions (solitons) and their moduli spaces, and special classes of field theories where the theory is completely solvable (integrable models).

Work on string theory has led to the discovery that some quantum field theories can be related to string theories in a space with more dimensions; this is referred to as holography. Some difficult questions in the field theory can be mapped to simpler questions in the higher-dimensional space. This also provides a new perspective on string theory, which can be used to deepen our understanding of gravity. We are studying the application of these techniques to field theories used to study interesting new phases of matter, and we are exploring the role of intrinsically quantum mechanical features of the field theory in the emergence of the higher-dimensional geometry.

Cosmology is the study of the very early universe. This has a long history of fruitful interaction with particle theory, and we are developing this further, relating new developments in field theory to cosmological observations. For example, we are studying the role of the Hiss boson recently discovered at CERN in cosmological evolution.

One strand of our research is the development of new tools for computations in quantum field theory. In one line of research, it has been understood that certain gauge theories have additional previously unsuspected symmetries, which explain the mysterious simplicity of some computational results. This has been developed to obtain more efficient calculational techniques for increasingly general questions. In an independent line, a symmetry called conformal symmetry has been newly exploited to constrain the particle content and interactions of theories with this symmetry. We aim to develop these tools further and bring them together with the long-term goal of completely solving the simplest, most symmetric theories. We also have a broad programme of research on aspects of field theory far from the vacuum, including work on smooth classical solutions (solitons) and their moduli spaces, and special classes of field theories where the theory is completely solvable (integrable models).

Work on string theory has led to the discovery that some quantum field theories can be related to string theories in a space with more dimensions; this is referred to as holography. Some difficult questions in the field theory can be mapped to simpler questions in the higher-dimensional space. This also provides a new perspective on string theory, which can be used to deepen our understanding of gravity. We are studying the application of these techniques to field theories used to study interesting new phases of matter, and we are exploring the role of intrinsically quantum mechanical features of the field theory in the emergence of the higher-dimensional geometry.

Cosmology is the study of the very early universe. This has a long history of fruitful interaction with particle theory, and we are developing this further, relating new developments in field theory to cosmological observations. For example, we are studying the role of the Hiss boson recently discovered at CERN in cosmological evolution.

### Planned Impact

Our work primarily has an academic impact, through the contribution to knowledge about the fundamental nature of forces and spacetime. This includes impact on related academic disciplines, where connections between different areas such as the holographic relations of field theories to gravity and new calculational techniques can be applied to study a wide range of questions, including aspects of the properties of matter with potential real-world implications. We have an active engagement with outreach activities at local, national and international levels which has an impact on school children and the public at large.

### Publications

Abl T
(2019)

*Recursion relations for anomalous dimensions in the 6d (2, 0) theory*in Journal of High Energy Physics
Ahmed W
(2019)

*Conical holographic heat engines*in Classical and Quantum Gravity
Anabalón A
(2018)

*Holographic thermodynamics of accelerating black holes*in Physical Review D
Anabalón A
(2019)

*Thermodynamics of charged, rotating, and accelerating black holes*in Journal of High Energy Physics
Andrei N
(2020)

*Boundary and defect CFT: open problems and applications*in Journal of Physics A: Mathematical and Theoretical
Appels M
(2017)

*Black hole thermodynamics with conical defects*in Journal of High Energy Physics
Aprile F
(2018)

*Unmixing supergravity*in Journal of High Energy Physics
Aprile F
(2020)

*One-loop amplitudes in AdS5×S5 supergravity from $$ \mathcal{N} $$ = 4 SYM at strong coupling*in Journal of High Energy Physics
Aprile F
(2018)

*Loop corrections for Kaluza-Klein AdS amplitudes*in Journal of High Energy Physics
Aprile F
(2018)

*Double-trace spectrum of N = 4 supersymmetric Yang-Mills theory at strong coupling*in Physical Review DDescription | LMS Scheme 3 Grant |

Amount | £1,200 (GBP) |

Funding ID | 31730 |

Organisation | London Mathematical Society |

Sector | Academic/University |

Country | United Kingdom |

Start | 10/2017 |

End | 09/2018 |

Description | Royal Society Research Fellow Enhancement Award |

Amount | £92,938 (GBP) |

Funding ID | RGF\EA\180182 |

Organisation | The Royal Society |

Sector | Charity/Non Profit |

Country | United Kingdom |

Start | 10/2018 |

End | 03/2023 |

Description | University Research Fellowships Renewals 2020 |

Amount | £395,868 (GBP) |

Funding ID | URF\R\201025 |

Organisation | The Royal Society |

Sector | Charity/Non Profit |

Country | United Kingdom |

Start | 10/2020 |

End | 09/2023 |

Description | International Particle Physics Masterclass |

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

Part Of Official Scheme? | No |

Geographic Reach | Regional |

Primary Audience | Schools |

Results and Impact | In March 2019, I helped organise an International Particle Physics masterclass in the IPPP at Durham University, where over 100 students analysed real data from the ATLAS detector in the LHC. This inspired many students to ask questions and have discussions. |

Year(s) Of Engagement Activity | 2019 |

Description | New Scientist - Instant Expert - "Relativity and Beyond" |

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

Part Of Official Scheme? | No |

Geographic Reach | National |

Primary Audience | Public/other audiences |

Results and Impact | Participated in a New Scientist event. Gave two talks and part of Panel discussion. |

Year(s) Of Engagement Activity | 2017 |

Description | School Outreach Program |

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

Part Of Official Scheme? | No |

Geographic Reach | Regional |

Primary Audience | Schools |

Results and Impact | I participated in a school outreach program called the Ordered Universe project in which 20 high school students visited the IPPP at Durham University and learned about exciting topics in particle physics like particle colliders and dark matter though a brief lecture and hands-on experiments. This inspired many students to ask questions and have discussions. |

Year(s) Of Engagement Activity | 2018 |