# Symmetries, Supersymmetries, Strings and Spacetime: the search for a fundamental theory of physics.

Lead Research Organisation:
King's College London

Department Name: Mathematics

### Abstract

The proposed research is part of a quest to find a single, complete and consistent theory of physics. While the electromagnetic, weak and strong forces have been understood since the formulation of the so-called standard model in 1967, it has so far not been possible also add the more familiar force of gravity in a consistent way. Our current description of gravity is Einstein's very successful theory of general relativity, which describes the motion of planets, stars and galaxies. At small distances the behaviour of matter and forces is governed by quantum mechanics. It is crucial for the quantum mechanical consistency of the electromagnetic and strong and weak forces that the standard model of particle physics incorporates a large amount of of symmetry. Unfortunately, Einstein's theory of general relativity is not consistent with quantum mechanics and so can not be simply combined with the standard model to provide a consistent theory of all the four forces. It is widely believed that supersymmetry, which is a symmetry that exchanges fermions (matter particles such as the electron) with bosons (force carriers such as photons of light) will play an important role in formulating a unified theory of the four forces. Supersymmetry predicts the existence of yet unknown subatomic particles, and the search for these is an important motivation behind the construction of the `Large Hadron Collider' (LHC) at CERN, a vast laboratory situated in Geneva. Strings are microscopic objects which are extended along one dimensions and can vibrate, just like strings on a violin. To date there does not exist a complete theory of strings, but the lowest energy effects of such a theory are unique as a consequence of the large amount of symmetry, and in particular supersymmetry, that they possess. These are the so-called supergravity theories. By studying these theories it has been realised that branes and a symmetry called U-duality are an important part of the full theory. Branes can similarly be thought of as microscopic generalizations of strings to objects that are extended along more than one dimension. We wish to find and understand this underlying theory of strings and branes. We propose to investigate this very intricate theory from several points of view. The first is to understand the theory at low energies, where it must produce spacetime and the four forces we know. Secondly, we will investigate the theory at very high energies, where its fundamental constituents behave like vibrating strings and branes and the notion of a smooth spacetime does no longer make sense. Our most important tool will be the enormous amount of symmetry that this theory is thought to possesses. Symmetry is a sign of underlying simplicity and beauty and has been a reliable guiding principle in reaching the understanding of physics we have today. In this process we expect to replace of our usual notion of spacetime by one which is consistent with such symmetries. This illustrates on the one hand the profound effect that a unified theory has on our understanding of nature, and on the other hand the central role played by symmetries.

### Organisations

- King's College London, United Kingdom (Collaboration, Lead Research Organisation)
- University of Oxford, United Kingdom (Collaboration)
- The Institut de Physique Théorique (IPhT) (Collaboration)
- Chalmers University of Technology, Sweden (Collaboration)
- European Organization for Nuclear Research (CERN) (Collaboration)
- PA Consulting Group (Collaboration)
- University of Groningen (Collaboration)
- City, University of London (Collaboration)
- Durham University, United Kingdom (Collaboration)
- University of Chicago, United States (Collaboration)
- Osaka City University (Collaboration)
- University of Pennsylvania, United States (Collaboration)
- Swansea University, United Kingdom (Collaboration)
- Stanford University, United States (Collaboration)
- Perimeter Institute for Theoretical Physics (Collaboration)
- Kavli Institute For Theoretical Physics (Collaboration)

### Publications

Chu X
(2011)

*Higgsing M2 to D2 with gravity: $ \mathcal{N} = 6 $ chiral supergravity from topologically gauged ABJM theory*in Journal of High Energy Physics
Cook P
(2009)

*Exotic E 11 branes as composite gravitational solutions*in Classical and Quantum Gravity
Couzens C
(2017)

*F-theory and AdS3/CFT2*in Journal of High Energy Physics
Deo J
(2011)

*Moduli stabilisation on the worldsheet*in Journal of High Energy Physics
Dolan M
(2011)

*F -theory GUTs with U ( 1 ) symmetries: Generalities and survey*in Physical Review D
Dolan M
(2011)

*Unification and LHC phenomenology of F-theory GUTs with U(1) P Q*in Journal of High Energy Physics
Dorn H
(2010)

*Space-like minimal surfaces in AdS × S*in Journal of High Energy Physics
Drukker N
(2017)

*The energy-momentum multiplet of supersymmetric defect field theories*in Journal of High Energy Physics
Drukker N
(2009)

*Loop operators and S-duality from curves on Riemann surfaces*in Journal of High Energy Physics
Drukker N
(2011)

*Nonperturbative aspects of ABJM theory*in Journal of High Energy PhysicsDescription | LMS "Scheme 2 Grant" |

Amount | £1,200 (GBP) |

Organisation | London Mathematical Society |

Sector | Learned Society |

Country | United Kingdom |

Start | 11/2010 |

End | 01/2011 |

Description | ATLAS Experiment (Bobby Acharya) |

Organisation | European Organization for Nuclear Research (CERN) |

Department | CERN LHC ATLAS |

Country | Switzerland |

Sector | Public |

PI Contribution | Phenomenology and Experiment |

Collaborator Contribution | Phenomenology and Experiment |

Impact | Discoveries in Particle Physics, as the Higgs Boson |

Start Year | 2008 |

Description | Black Holes and Spinorial Geometry |

Organisation | Chalmers University of Technology |

Department | Department of Fundamental Physics |

Country | Sweden |

Sector | Academic/University |

PI Contribution | We have developed techniques so solve the Killing spinor equations of supergravity theories leading to a systematic classification the gravitational solitons, instantons, black holes and compactification vacua with applications in strings, gauge/gravity dualities and M-theory. |

Collaborator Contribution | This collaboration assisted with the technical issues of the project and helped with the dissemination of the results. |

Impact | It has resulted in writing more than 25 papers, more than 10 since 2008, published in highly regarded international journals. I have presented the results in more than 5 conferences since 2008 and similar numbers apply to my collaborators. |

Description | Black Holes and Spinorial Geometry |

Organisation | King's College London |

Department | Department of Mathematics |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | We have developed techniques so solve the Killing spinor equations of supergravity theories leading to a systematic classification the gravitational solitons, instantons, black holes and compactification vacua with applications in strings, gauge/gravity dualities and M-theory. |

Collaborator Contribution | This collaboration assisted with the technical issues of the project and helped with the dissemination of the results. |

Impact | It has resulted in writing more than 25 papers, more than 10 since 2008, published in highly regarded international journals. I have presented the results in more than 5 conferences since 2008 and similar numbers apply to my collaborators. |

Description | Black Holes and Spinorial Geometry |

Organisation | University of Groningen |

Department | Centre for Theoretical Physics |

Country | Netherlands |

Sector | Academic/University |

PI Contribution | We have developed techniques so solve the Killing spinor equations of supergravity theories leading to a systematic classification the gravitational solitons, instantons, black holes and compactification vacua with applications in strings, gauge/gravity dualities and M-theory. |

Collaborator Contribution | This collaboration assisted with the technical issues of the project and helped with the dissemination of the results. |

Impact | It has resulted in writing more than 25 papers, more than 10 since 2008, published in highly regarded international journals. I have presented the results in more than 5 conferences since 2008 and similar numbers apply to my collaborators. |

Description | Correlation functions of twist fields in 2-d QFT |

Organisation | Durham University |

Department | Department of Mathematical Sciences |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | I have set-up and led the project, provided the solution technique, and provided the full conformal field theoretic calculation |

Collaborator Contribution | PhD Student |

Impact | One significant paper was published; I presented the results at various seminars (both in UK and abroad), and my student presented the results at the conference "Integrable and conformal field theory 2011", City University London. |

Start Year | 2009 |

Description | Dynamical Supersymmetry breaking |

Organisation | Kavli Institute For Theoretical Physics |

Country | United States |

Sector | Academic/University |

PI Contribution | Schafer-Nameki, Tamarit and Torroba have found various approaches to address naturalness in dynamical supersymmetry breaking models, in particular ISS type supersymmetry breaking. |

Impact | Talk at String Pheno 2010. |

Start Year | 2009 |

Description | Dynamical Supersymmetry breaking |

Organisation | Stanford University |

Department | Department of Physics |

Country | United States |

Sector | Academic/University |

PI Contribution | Schafer-Nameki, Tamarit and Torroba have found various approaches to address naturalness in dynamical supersymmetry breaking models, in particular ISS type supersymmetry breaking. |

Impact | Talk at String Pheno 2010. |

Start Year | 2009 |

Description | Entanglement entropy in quantum field theory |

Organisation | City, University of London |

Department | Department of Mathematics |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | significant intellectual input (collaborators made equal contribution to the research). |

Collaborator Contribution | Significant intellectual input at the start of the collaboration and various discussions ever since |

Impact | This collaboration has led to 6 significant papers since its beginning (5 since 2008, 1 since arrival at King's, 2010), as well as international recognition (including being scientific editor for a book series on the subject, pre-arrival at King's). |

Start Year | 2007 |

Description | Entanglement entropy in quantum field theory |

Organisation | University of Oxford |

Department | Rudolf Peierls Centre for Theoretical Physics |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | significant intellectual input (collaborators made equal contribution to the research). |

Collaborator Contribution | Significant intellectual input at the start of the collaboration and various discussions ever since |

Impact | This collaboration has led to 6 significant papers since its beginning (5 since 2008, 1 since arrival at King's, 2010), as well as international recognition (including being scientific editor for a book series on the subject, pre-arrival at King's). |

Start Year | 2007 |

Description | F-theory and String Phenomenology |

Organisation | Durham University |

Department | Institute for Particle Physics Phenomenology (IPPP) |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | Marsao, Saulina and Schafer-Nameki are one of the main collaborations studying F-theory compactifications in the light of string phenomenology. Recently the collaboration was joined by Dolan from Durham, to study the implication of this work for the LHC. |

Impact | The work has been widely recognized, in particular by two invited talks at the annual Strings conferences. |

Start Year | 2008 |

Description | F-theory and String Phenomenology |

Organisation | Perimeter Institute for Theoretical Physics |

Country | Canada |

Sector | Multiple |

PI Contribution | Marsao, Saulina and Schafer-Nameki are one of the main collaborations studying F-theory compactifications in the light of string phenomenology. Recently the collaboration was joined by Dolan from Durham, to study the implication of this work for the LHC. |

Impact | The work has been widely recognized, in particular by two invited talks at the annual Strings conferences. |

Start Year | 2008 |

Description | F-theory and String Phenomenology |

Organisation | University of Chicago |

Department | Department of Physics |

Country | United States |

Sector | Academic/University |

PI Contribution | Marsao, Saulina and Schafer-Nameki are one of the main collaborations studying F-theory compactifications in the light of string phenomenology. Recently the collaboration was joined by Dolan from Durham, to study the implication of this work for the LHC. |

Impact | The work has been widely recognized, in particular by two invited talks at the annual Strings conferences. |

Start Year | 2008 |

Description | Fivebranes and resolved deformed G_2 manifolds |

Organisation | Swansea University |

Department | Department of Physics |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | I set up the problem, and carried out most of the analytic calculations involved. |

Collaborator Contribution | I have led this project, in collaboration with a PhD student at Swansea University. |

Impact | Results of this collaboration were presented by myself at the annual Strings 2010 conference. |

Start Year | 2010 |

Description | Integrability and AdS/CFT: 3-point functions |

Organisation | Perimeter Institute for Theoretical Physics |

Country | Canada |

Sector | Multiple |

PI Contribution | significant intellectual input |

Collaborator Contribution | significant intellectual input |

Impact | 3-point function at tree level and its quasi-classical limit. When combined with the known results at strong coupling could lead to the complete solution of N=4 SYM theory in 4D in planar limit. |

Start Year | 2010 |

Description | Integrability and AdS/CFT: Y-system, Quantum spectral curve |

Organisation | Moscow State University |

Department | Physics Department |

Country | Russian Federation |

Sector | Academic/University |

PI Contribution | Significant intellectual input into my collaborators research |

Collaborator Contribution | significant intellectual input |

Impact | Recent results: 1) Numerical results for nonperturbative spectrum of N=4 SYM 2) Analytical confirmation of previous numerical results at strong coupling of N=4 SYM 3) Proposed spectral equations for beta-deformed Super Yang-Mills 4) Results were reported at Strings 2010, (and 2009) and 2014 by N. Gromov 5) Quantum spectral curve developed for all local operators of the theory 6) Results of the pure QCD are reproduced using these new methods 7) the interpolation function in ABJM theory is found explicitly Before joining King's college: The Y-system and TBA equations were conjectured and tested in many various ways. The equations should give the exact solution of the spectral problem of 4D planar N=4 SYM. |

Start Year | 2006 |

Description | Integrability and AdS/CFT: Y-system, Quantum spectral curve |

Organisation | Osaka City University |

Department | Advanced Mathematical Institute |

Country | Japan |

Sector | Academic/University |

PI Contribution | Significant intellectual input into my collaborators research |

Collaborator Contribution | significant intellectual input |

Impact | Recent results: 1) Numerical results for nonperturbative spectrum of N=4 SYM 2) Analytical confirmation of previous numerical results at strong coupling of N=4 SYM 3) Proposed spectral equations for beta-deformed Super Yang-Mills 4) Results were reported at Strings 2010, (and 2009) and 2014 by N. Gromov 5) Quantum spectral curve developed for all local operators of the theory 6) Results of the pure QCD are reproduced using these new methods 7) the interpolation function in ABJM theory is found explicitly Before joining King's college: The Y-system and TBA equations were conjectured and tested in many various ways. The equations should give the exact solution of the spectral problem of 4D planar N=4 SYM. |

Start Year | 2006 |

Description | Integrability and AdS/CFT: Y-system, Quantum spectral curve |

Organisation | The Institut de Physique Théorique (IPhT) |

Country | France |

Sector | Academic/University |

PI Contribution | Significant intellectual input into my collaborators research |

Collaborator Contribution | significant intellectual input |

Impact | Recent results: 1) Numerical results for nonperturbative spectrum of N=4 SYM 2) Analytical confirmation of previous numerical results at strong coupling of N=4 SYM 3) Proposed spectral equations for beta-deformed Super Yang-Mills 4) Results were reported at Strings 2010, (and 2009) and 2014 by N. Gromov 5) Quantum spectral curve developed for all local operators of the theory 6) Results of the pure QCD are reproduced using these new methods 7) the interpolation function in ABJM theory is found explicitly Before joining King's college: The Y-system and TBA equations were conjectured and tested in many various ways. The equations should give the exact solution of the spectral problem of 4D planar N=4 SYM. |

Start Year | 2006 |

Description | Integrability and AdS/CFT: Y-system, Quantum spectral curve |

Organisation | University of Pennsylvania |

Department | Department of Physics & Astronomy |

Country | United States |

Sector | Academic/University |

PI Contribution | Significant intellectual input into my collaborators research |

Collaborator Contribution | significant intellectual input |

Impact | |

Start Year | 2006 |

Description | Non-Kahler heterotic rotations |

Organisation | University of Oxford |

Department | Mathematical Institute Oxford |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | I and my collaborator have made equal contributions to this project. All calculations are carried out independently by the collaborators. |

Collaborator Contribution | I and my collaborator have made equal contributions to this project. All calculations are carried out independently by the collaborators. |

Impact | Obtained novel results about heterotic string theory. |

Start Year | 2010 |

Description | The large N limit of quiver matrix models and Sasaki-Einstein manifolds |

Organisation | University of Oxford |

Department | Mathematical Institute Oxford |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | Both collaborators made equal contributions to the research. |

Collaborator Contribution | Both collaborators made equal contributions to the research. |

Impact | Very interesting new results in AdS/CFT were obtained. |

Start Year | 2011 |

Description | The warped, resolved, deformed conifold gets flavoured |

Organisation | Swansea University |

Department | Department of Physics |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | I have particularly contributed to carrying out the supergravity computations involving geometric techniques. |

Collaborator Contribution | Complementary knowledge led to broader results within the collaboration. |

Impact | Results have been presented by myself at the annual Strings 2010 conference. Led to further developments addressed in subsequent joint work. |

Start Year | 2010 |

Description | Newspaper interview |

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

Part Of Official Scheme? | No |

Primary Audience | Media (as a channel to the public) |

Results and Impact | Invited interviews by journalists working for newspapers. General public took interest in theoretical physics and science in general. |

Year(s) Of Engagement Activity | 2010,2011 |

Description | School Visit |

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

Part Of Official Scheme? | No |

Primary Audience | Schools |

Results and Impact | 2-3 groups of approximately 20 A-level students came to King's College and were given a presentation on aspects of modern mathematics including Theoretical Physics. On two other occasions members of the group went to their old schools to give a presentation on Theoretical Physics. These presentations were very well received and encourgaged several students to take Physics courses at university. |

Year(s) Of Engagement Activity | 2008,2009,2010 |

Description | radio interview |

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

Part Of Official Scheme? | No |

Primary Audience | Public/other audiences |

Results and Impact | gave description of string theory people commented on it |

Year(s) Of Engagement Activity | 2010 |

Description | reference in popular novel |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Primary Audience | Public/other audiences |

Results and Impact | Research work of Lambert was featured in the novel 'Solar' by E. Mcewan The book is by one of the UK's leading authors and has been widely read through-out the world. It's theme centres around topics of modern science and in paritcular climate change but also mentioned the work of Lambert in M-theory. |

Year(s) Of Engagement Activity | 2010 |