# Summaries

## STFC Consolidated Grant 2017-2020: Particles, Fields and Spacetime

(PI: Simon Ross)

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.

## STFC Consolidated Grant 2014-2017: Particles, Fields and Spacetime

(PI: Simon Ross)

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.

The grant is awarded to the members of the Centre for Particle Theory who are also staff in the Department of Mathematical Sciences.

## Leverhulme Trust Research Programme Grant: SPOCK: Scientific Properties Of Complex Knots

(PI: Paul Sutcliffe)

The complexity of three-dimensional systems is often topological: spatial systems of filaments, dynamically evolving, typically become tangled and knotted in a way that reveals underlying properties of the system. The aim of the project is to create new computational tools and mathematical techniques for the analysis, synthesis and exploitation of knotted structures in a wide range of complex physical phenomena, allowing the development of a deep understanding of topological complexity in nature. This will require new mathematical techniques beyond traditional (abstract) knot theory, which will be developed as a generic Topological Toolkit to synthesize and analyse knotted physical systems. The main question is where and how knots arise in nature, including how the background environment (designed or otherwise) can influence the generation of knotted structures. A driving force for this development is new analytical, numerical and experimental techniques in a number of carefully selected interdisciplinary sub-projects, where experimentalists, theorists, mathematicians and scholars from the humanities can work together in identifying and solving problems in applied knot theory.

This collaboration between Durham University and the University of Bristol, with the award including funding for 4 Research Associates for 4 years and 8 PhD students, divided equally between the two Universities.

## ERC Consolidator Grant 2014-2019: SPiN: Symmetry Principles in Nature

(PI: Mukund Rangamani)

Symmetries have traditionally played a very important role in our understanding of physics, both classical and quantum. As we move towards the next frontier of defining a quantum theory of gravity, it is clear that they will continue to play a predominant role. The current project is aimed at obtaining a comprehensive understanding of the dynamics of strongly coupled quantum systems, exploiting various symmetry properties that one expects on physical grounds. Specifically, the aim is to come up with effective descriptions of a wide class of quantum dynamics in gravitational and non-gravitational theories using the holographic gauge/gravity correspondence.

One of the primary strands of the proposed research involves a critical examination of gravitational theories with higher spin symmetry. We will investigate the phase structure of such theories, the nature of gravitational solutions and notions of classical geometry in the presence of the enlarged gauge symmetry. Using appropriate generalizations of the gauge/gravity correspondence we will try to give gauge invariant characterizations of these concepts and further explore how such higher spin theories can be realized in string theory. A related strand of research concerns a deeper understanding of the gauge/gravity correspondence itself, with focus on figuring out how collective behaviour of strongly coupled field theories leads to the emergence of extra symmetries, such as local diffeomorphisms in the dual description. Along the way we will also develop effective descriptions for collective dynamics of strongly coupled quantum degrees of freedom, both in and out of equilibrium.

## ERC Consolidator Grant 2014-2019: NuMass: Neutrinos: a different portal to new physics Beyond the Standard Model

(PI: Silvia Pascoli)

The NuMass project focuses on new physics at low energy scales, below the one reachable at the LHC. This approach is complementary to the energy frontier in the search for new physics beyond the Standard Model. The underlying idea is that new particles could be hidden not because they are too heavy but because, although light, they interact too weakly with ordinary matter. Neutrinos are by far the least understood of the standard fermions: if new particles are indeed at low scales, below the electroweak one, a likely scenario is that they couple more strongly to neutrinos than to other standard particles, e.g. quarks. The NuMass project will use neutrinos as a portal into new physics and will combine theory, phenomenology and cosmology, from proposing theoretical models to testing their signatures and understanding their cosmological consequences.

## ERC Advanced Grant 2014-2019: McatNNLO: High Precision Simulation of Particle Collisions at the LHC

(PI: Nigel Glover)

McatNNLO aims to make more precise predictions for physical observables at the LHC and other particle collider experiments, thereby leading to a more precise extraction of fundamental physics parameters, such as the couplings of the Higgs boson to other fundamental particles.

## EU Initial Training Network 2014-2018: Higgstools

(Network Coordinator: Nigel Glover)

The research goal of Higgstools is the investigation of electroweak symmetry breaking. The main aim of the project is to provide excellent initial training to young researchers. The network involves 10 teams from 37 Universities and Institutes worldwide.

## EU Initial Training Network 2013-2017: Mcnet

(Local Coordinator: Peter Richardson)

Mcnet is dedicated to developing and supporting general-purpose Monte-Carlo event generators throughout the LHC era and beyond, training a wide selection of its user base, particularly through funded short-term `residencies' and annual schools. This network involves 8 leading research centres (Manchester, CERN, Durham, Gottingen, Karlsruhe, Louvain, Lund, UCL).

## EU Initial Training Network 2012-2016: GATIS: Gauge Theory as an Integrable System

(Local Coordinator: Patrick Dorey)

Gauge Theories provide the most successful framework for the description of nature, and in particular of high energy physics. However, extracting reliable predictions relevant for experiment from gauge theory has remained a major challenge which so far requires massive use of computer algebra. Over the last decade an entirely new approach to quantum gauge theories has begun to emerge, initiated by a celebrated duality between gauge and string theory. This has brought an area of science into gauge theory that seemed unrelated a few years before, namely the theory of low-dimensional statistical systems and strongly correlated electron systems. The paradigm governing this is to view "Gauge Theory as an Integrable System". The partners of this network represent different communities from gauge theory, statistical physics and computer algebra. With the proposed Initial Training Network we will carry the emerging multidisciplinary interaction to an entirely new level, bridging the gaps between our research fields in the context of graduate training activity. We believe that coordinated education of young scientists in all the tools under development from the different communities offers tremendous potential to make progress in the understanding and application of gauge theory. A group of carefully selected private sector partners will assist dissemination of results, methods and ideas into neighboring scientific disciplines as well as to the general public. At the same time, they will also be vital in preparing the early stage researchers for active and leading roles in academia and beyond.

The GATIS network is composed of seven nodes. Each node includes research teams in theoretical physics.

## EU Initial Training Network 2011-2015: Invisibles

(UK Coordinator: Silvia Pascoli)

Invisibles focuses on Neutrino and Dark matter phenomenology and their connection. Experimental and theoretical aspects are also encompassed. The network involves 7 European and 7 non-European partners.

## EU Initial Training Network 2011-2015: LHCphenonet

(UK Coordinator: Daniel Maitre)

LHCphenonet performs advanced particle phenomenology in the LHC era. The consortium consists of 12 teams from 28 European Universities and Research Institutes, the University of Buenos Aires, CERN, and 3 partners from the industrial sector.