Particles, Fields and Spacetime

Lead Research Organisation: Durham University
Department Name: Mathematical Sciences

Abstract

Particle Physics has entered a new and crucial phase. The Large Hadron Collider at CERN has enabled us to examine experimentally theoretical concepts that underly the standard model of particle physics, such as the Higgs mechanism, and it will go on to search for the deeper structures that are believed to unify the laws of physics.

Quantum field theory is the mathematical language in which the standard model is expressed, and it treats particles as point-like objects. Only certain kinds of quantum field theories, known as gauge theories, are consistent in the four dimensional world we live in. These include, and are generalisations of, the theory of electrodynamics that describes light interacting with electric charge. To be able to interpret the results of experiments we need to be able to solve gauge theories, at least approximately. This is a hard problem, but one in which there has recently been very remarkable progress due to a convergence of ideas originally developed in quite disparate contexts for solving very different kinds of theories. A major thrust of the project will be to push this line of enquiry further so as to be able to more fully understand gauge theories and be able to compute their properties.

Matter at large scales is dominated by gravity which is described by Einstein's theory of General Relativity. This governs the motion of planets, stars, galaxies, and the evolution of the Universe itself. Uniting General Relativity and the standard model of particle physics is the most important challenge facing theoretical physics. It is widely, though not universally, believed that string theory provides such a unification. String theory replaces the point-like particles of quantum field theory with extended objects whose different vibrational modes account for the different species of fundamental particles. It is this belief that leads to the expectation that supersymmetry, a property of all realistic string theories, plays a role in nature, and may well be discovered at the LHC. Showing how nature contrives to hide this property is another part of the project.

String theory has also led to many unexpected relations between different kinds of physical theories, most notably in the AdS/CFT correspondence which states equivalences between certain gravity theories and corresponding gauge theories, enabling us to solve difficult problems in one theory by studying simper ones in the other. We will use this to study problems in gravity that would otherwise be intractable and also model strongly coupled physical processes in diverse areas ranging from condensed matter physics to plasmas by gravity.

We will also use another method for studying hadrons that is particularly appropriate to describing large numbers of thembound into nuclei or even neutron stars. This is based on effective field theories such as the Skyrme model which we will investigate numerically using computers.

Being a theory of quantum gravity strings have many implications for cosmology, in particular they admit the possibility that what we see as the physical universe is only a low dimensional subspace called a brane, moving in a space of higher dimensions. We will continue the quest to find direct experimental and observational signatures that will test this scenario.

Planned Impact

Our principal impact results from training substantial numbers of PhD students and PDRAs whose exposure to fundamental research enables them to develop analytical skills that they continue to use when they leave us, either in academic life or industry. Additionally our research has impact on other academic disciplines notably pure mathematics, and biology where we export field theoretic methods to solve biological problems. We have a small engagement with industry via applications of field theory to model foams used in manufacturing. We are also engaged in outreach at local, national and international levels which has an impact on school children and the public at large.

Publications

10 25 50
publication icon
Alexander H (2015) Alice and Bob in an expanding spacetime in EPL (Europhysics Letters)

publication icon
Alexander H (2016) Entanglement of self-interacting scalar fields in an expanding spacetime in EPL (Europhysics Letters)

publication icon
Ambrosio R (2015) Local integrands for the five-point amplitude in planar N=4 SYM up to five loops in Journal of High Energy Physics

publication icon
Andrade T (2015) Schrödinger holography for z < 2 in Classical and Quantum Gravity

publication icon
Andrade T (2015) Schrödinger holography with z = 2 in Classical and Quantum Gravity

publication icon
Appels M (2017) Black hole thermodynamics with conical defects in Journal of High Energy Physics

publication icon
Appels M (2016) Thermodynamics of Accelerating Black Holes. in Physical review letters

publication icon
Armas J (2016) Surface transport in plasma-balls in Journal of High Energy Physics

publication icon
Arthur R (2016) Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions in Journal of Physics A: Mathematical and Theoretical

publication icon
Balasubramanian V (2017) Entanglement shadows in LLM geometries in Journal of High Energy Physics

 
Description Amplitudes, Strings and Branes
Amount £421,448 (GBP)
Funding ID UF140541 
Organisation The Royal Society 
Sector Charity/Non Profit
Country United Kingdom
Start 10/2015 
End 09/2020
 
Description Consolidated grant
Amount £502,732 (GBP)
Funding ID ST/P000371/1 
Organisation Science and Technologies Facilities Council (STFC) 
Sector Public
Country United Kingdom
Start 10/2017 
End 09/2020
 
Description LMS Scheme 3 Grant
Amount £1,500 (GBP)
Funding ID 31431 
Organisation London Mathematical Society 
Sector Academic/University
Country United Kingdom
Start 10/2014 
End 09/2015
 
Description LMS Scheme 3 Grant
Amount £1,200 (GBP)
Funding ID 31635 
Organisation London Mathematical Society 
Sector Academic/University
Country United Kingdom
Start 10/2016 
End 09/2017
 
Description NUTS: Nuclei using Topological Solitons
Amount £139,580 (GBP)
Funding ID 702329 
Organisation European Commission 
Sector Public
Country European Union (EU)
Start 10/2016 
End 09/2018
 
Description North British Mathematical Physics Seminar
Amount £1,500 (GBP)
Funding ID 31532 
Organisation London Mathematical Society 
Sector Academic/University
Country United Kingdom
Start 10/2015 
End 09/2016
 
Title Cadabra II 
Description Cadabra is a symbolic computer algebra system (CAS) designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor computer algebra, tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, component computations, implicit coordinate dependence, multiple index types and many more. The input format is a subset of TeX. Both a command-line and a graphical interface are available. Version II is a rewrite of software originally published in 2007, with many enhancements and new features. 
Type Of Technology Software 
Year Produced 2016 
Open Source License? Yes  
Impact Since the release of version II, nearly 400 users have registered with their email address, and about 60 research papers have cited the software. 
URL https://cadabra.science
 
Description BBC Radio 4: "In Our Time'': (Einstein), 6/6/13 
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 Media (as a channel to the public)
Results and Impact In Our Time program - garnered usual public interest
Year(s) Of Engagement Activity 2013
 
Description BBC Radio 4: In Our Time'': (Perpetual Motion), 24/9/15 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact Participation in R4 Programme - follow up calls and interest from general public
Year(s) Of Engagement Activity 2015
 
Description Hack Circus - TIme 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact Actual plus social media event
Year(s) Of Engagement Activity 2013
URL https://www.youtube.com/user/hackcircus
 
Description Lectures at the African Institute for Mathematical Sciences (AIMS) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Lectured African students at AIMS (South Africa and Ghana) on "Solitons"; cohort from 30 to 50 each time. In 2011 in addition gave a public lecture for the Cape Town Science Centre's "Science Out Loud" lecture series, "The soliton: John Scott Russell's Great Wave of Translation", audience the general public, about 60 strong.
Year(s) Of Engagement Activity 2007,2008,2009,2010,2011,2012,2013,2015,2016
URL http://nexteinstein.org
 
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