# Symmetry, supersymmetry, strings, branes and gauge theories; physics from the Planck to the QCD scale.

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

standard model in 1967, it has so far not been possible

to 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 cannot 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 dimension 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. This complete theory is known as M-theory. Although little is known about it on microscopic level it is known to involve eleven-dimensions, extending the ten-dimensional space-time of superstrings.

We wish to find and understand this underlying theory of string 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 space-time 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 space-time 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 space-time

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.

and consistent theory of physics. While the electromagnetic, weak

and strong forces have been understood since the formulation of the

standard model in 1967, it has so far not been possible

to 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 cannot 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 dimension 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. This complete theory is known as M-theory. Although little is known about it on microscopic level it is known to involve eleven-dimensions, extending the ten-dimensional space-time of superstrings.

We wish to find and understand this underlying theory of string 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 space-time 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 space-time 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 space-time

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.

### Planned Impact

The proposed research will benefit most directly those working on

theoretical physics, in particular on supersymmetry and string

theory and more generally those seeking to find a single consistent

theory of physics. There are several research groups working on these topics within the UK and many more worldwide. The work involves some of the latest mathematics, hence is also

relevant to mathematicians, in particular those working on group

theory and geometry. However, such research also has direct

relevance to those working on the following fields: the strong nuclear force, the formulation of explicit phenomenological models of

particle physics, and the formulation of cosmological models of inflation and dark

matter. Thus it can also lead to benefits for model builders working on particle physics and astronomy. We have discussed the impact on these groups in the section `academic beneficiaries'.

Past work on theoretical physics has, with the fullness of time, been of considerable use to society either as a direct result of

the new physics found or as a consequence of the new mathematics and

technical developments that where developed. This has lead to a direct technological input into industry.

Industry also benefits from the training of young researchers in the ability to solve hard and complex problems. The theoretical physics group at King's has trained many younger researchers who have later entered the financial and other sectors

of the economy to apply their problem solving skills. In particular, by funding cutting edge science the UK attracts younger intellectual talent from both within and outside the UK. And although some carry on in UK academic life, a substantial number take non-academic jobs in the UK, thus providing the economy with highly trained people. Such spin-offs from fundamental science have long been vital to the international economic and industrial competitiveness that the UK enjoys. Indeed, a crucial feature of the modern UK's economic and social wealth is its international reputation as a world leader for independent thinking in both the academic and industrial sectors.

In addition to these economic factors, the general public has strong interest in the fundamental questions about our Universe. For example Lambert's work on M2-branes has appeared in the book `Solar' by Ian McEwan, showing a direct impact of the group's research into contemporary culture. The general public will therefore benefit from a deeper and continuing investigation into Nature at its smallest scales.

In summary, the UK can be proud of having one the worlds most prestigious and world leading scientific traditions which has long been a cornerstone of the UK's intellectual health, economic wealth and culture. We believe our proposed research is very much a part of this.

theoretical physics, in particular on supersymmetry and string

theory and more generally those seeking to find a single consistent

theory of physics. There are several research groups working on these topics within the UK and many more worldwide. The work involves some of the latest mathematics, hence is also

relevant to mathematicians, in particular those working on group

theory and geometry. However, such research also has direct

relevance to those working on the following fields: the strong nuclear force, the formulation of explicit phenomenological models of

particle physics, and the formulation of cosmological models of inflation and dark

matter. Thus it can also lead to benefits for model builders working on particle physics and astronomy. We have discussed the impact on these groups in the section `academic beneficiaries'.

Past work on theoretical physics has, with the fullness of time, been of considerable use to society either as a direct result of

the new physics found or as a consequence of the new mathematics and

technical developments that where developed. This has lead to a direct technological input into industry.

Industry also benefits from the training of young researchers in the ability to solve hard and complex problems. The theoretical physics group at King's has trained many younger researchers who have later entered the financial and other sectors

of the economy to apply their problem solving skills. In particular, by funding cutting edge science the UK attracts younger intellectual talent from both within and outside the UK. And although some carry on in UK academic life, a substantial number take non-academic jobs in the UK, thus providing the economy with highly trained people. Such spin-offs from fundamental science have long been vital to the international economic and industrial competitiveness that the UK enjoys. Indeed, a crucial feature of the modern UK's economic and social wealth is its international reputation as a world leader for independent thinking in both the academic and industrial sectors.

In addition to these economic factors, the general public has strong interest in the fundamental questions about our Universe. For example Lambert's work on M2-branes has appeared in the book `Solar' by Ian McEwan, showing a direct impact of the group's research into contemporary culture. The general public will therefore benefit from a deeper and continuing investigation into Nature at its smallest scales.

In summary, the UK can be proud of having one the worlds most prestigious and world leading scientific traditions which has long been a cornerstone of the UK's intellectual health, economic wealth and culture. We believe our proposed research is very much a part of this.

### Organisations

- King's College London, United Kingdom (Lead Research Organisation)
- The Institut de Physique Théorique (IPhT) (Collaboration)
- Max Planck Society (Collaboration)
- European Cooperation in Science and Technology (COST) (Collaboration)
- University of Bologna, Italy (Collaboration)
- European Organization for Nuclear Research (CERN) (Collaboration)
- University of Geneva, Switzerland (Collaboration)
- PA Consulting Group (Collaboration)
- Humboldt University Berlin, Germany (Collaboration)
- Osaka City University (Collaboration)
- University of Pennsylvania, United States (Collaboration)
- University of Turin (Collaboration)
- Perimeter Institute for Theoretical Physics (Collaboration)
- University of Tokyo (Collaboration)

### Publications

Aad G
(2011)

*Measurements of underlying-event properties using neutral and charged particles in pp collisions at $\sqrt{s}=900$ GeV and $\sqrt{s}=7$ TeV with the ATLAS detector at the LHC*in The European Physical Journal C
Aad G
(2011)

*Measurement of dijet azimuthal decorrelations in pp collisions at sqrt(s)=7 TeV.*in Physical review letters
Aad G
(2012)

*Jet mass and substructure of inclusive jets in $ \sqrt {s} = 7\;{\text{TeV}} $ pp collisions with the ATLAS experiment*in Journal of High Energy Physics
Aad G
(2013)

*Measurement of top quark polarization in top-antitop events from proton-proton collisions at vs=7 TeV using the ATLAS detector.*in Physical review letters
Aad G
(2011)

*A search for new physics in dijet mass and angular distributions in pp collisions at \sqrt{s}=7 TeV measured with the ATLAS detector*in New Journal of Physics
Aad G
(2011)

*Search for stable hadronising squarks and gluinos with the ATLAS experiment at the LHC*in Physics Letters B
Aad G
(2012)

*Search for supersymmetry in events with three leptons and missing transverse momentum in v[s]=7 TeV pp collisions with the ATLAS detector.*in Physical review letters
Aad G
(2012)

*Forward-backward correlations and charged-particle azimuthal distributions in pp interactions using the ATLAS detector*in Journal of High Energy Physics
Aad G
(2011)

*Luminosity determination in pp collisions at $\sqrt{s} = 7$ TeV using the ATLAS detector at the LHC*in The European Physical Journal CDescription | GATIS - Gauge Theory as an Integrable System |

Amount | £511,137 (GBP) |

Funding ID | FP7/2007-2013 Grant Agreement no.320769 |

Organisation | Marie Sklodowska-Curie Actions |

Sector | Charity/Non Profit |

Country | Global |

Start | 01/2013 |

End | 12/2016 |

Description | HOLOGRAV (small conference grant, spent in LPT ENS, not sure this is relevant) |

Amount | € 5,000 (EUR) |

Funding ID | 5175 |

Organisation | European Science Foundation (ESF) |

Sector | Charity/Non Profit |

Country | France |

Start | 08/2014 |

End | 09/2014 |

Description | Integrability workshop Israel |

Amount | 25,000 ש"ח (ILS) |

Organisation | The Israel Institute for Advanced Studies |

Sector | Academic/University |

Country | Israel |

Start | 03/2012 |

End | 06/2012 |

Description | LMS Conference Grant: MOST (Mathematics of String Theory) |

Amount | £4,400 (GBP) |

Funding ID | 11349 |

Organisation | London Mathematical Society |

Sector | Academic/University |

Country | United Kingdom |

Start | 04/2014 |

End | 05/2014 |

Description | Scheme 4 Grant (Work in paris, Gromov+Volin) |

Amount | £700 (GBP) |

Funding ID | 41212 |

Organisation | London Mathematical Society |

Sector | Academic/University |

Country | United Kingdom |

Start | 10/2012 |

End | 10/2013 |

Description | Visiting fellowship to SFB Hamburg |

Amount | € 5,750 (EUR) |

Organisation | University of Hamburg |

Sector | Academic/University |

Country | Germany |

Start | 07/2012 |

End | 04/2013 |

Description | ABJM |

Organisation | University of Geneva |

Department | Section of Mathematics |

Country | Switzerland |

Sector | Academic/University |

PI Contribution | I've collaborated with Members of the University of Geneva in writing a manuscript to be submitted to a journal soon. |

Collaborator Contribution | We collaborated on writing a paper and they invited me to Geneva for that purpose for a week. |

Impact | two papers: Commun.Math.Phys. 306 (2011) 511-563 and JHEP 1111 (2011) 141 |

Start Year | 2009 |

Description | AGT |

Organisation | Humboldt University of Berlin |

Department | Institute of Physics |

Country | Germany |

Sector | Academic/University |

PI Contribution | I've collaborated on the project with Filippo Passerini. |

Collaborator Contribution | I have collaborated with a member of Humboldt University in Berlin on writing a paper which is out as a preprint and in the process of being refereed for JHEP. We are currently collaborating on several further projects. |

Impact | paper: JHEP 1104 (2011) 106 |

Start Year | 2010 |

Description | COST Action "The String Theory Universe" |

Organisation | European Cooperation in Science and Technology (COST) |

Country | Belgium |

Sector | Public |

PI Contribution | Dr Schafer-Nameki is a core member of the COST action "The String Theory Universe". This funds workshops and research visits. Dr Schafer-Nameki organized through this COST action a workshop "Supersymmetry Breaking in String Theory" at the Isaac Newton Institute, Cambridge, March 10-14, 2014. In Oct 2015 she is organizing a school and workshop through the COST for two weeks at the Galileo Galilei Institute in Florence, Italy. |

Collaborator Contribution | Workshops and researcher visits. |

Impact | Past: Workshop "Supersymmetry Breaking in String Theory" at the Isaac Newton Institute, Cambridge, March 10-14, 2014. Future: School and Workshop on String Phenomenology at the Galileo Galilei Institute, Florence, Oct 19-30, 2015. |

Start Year | 2013 |

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

Organisation | Perimeter Institute for Theoretical Physics |

Country | Canada |

Sector | Academic/University |

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 | Quantum spectral curve for ABJM theory |

Organisation | University of Bologna |

Country | Italy |

Sector | Academic/University |

PI Contribution | Essential intellectual contribution: |

Collaborator Contribution | Essential intellectual contribution |

Impact | 10.1103/PhysRevLett.113.021601 One more in preparation |

Start Year | 2013 |

Description | Quantum spectral curve for ABJM theory |

Organisation | University of Turin |

Country | Italy |

Sector | Academic/University |

PI Contribution | Essential intellectual contribution: |

Collaborator Contribution | Essential intellectual contribution |

Impact | 10.1103/PhysRevLett.113.021601 One more in preparation |

Start Year | 2013 |

Description | Vortices |

Organisation | European Organization for Nuclear Research (CERN) |

Department | Theoretical Physics Unit |

Country | Switzerland |

Sector | Academic/University |

PI Contribution | I participated in writing a paper on vortex loop operators with Filippo Passerini and Takuya Okuda. I did 1/3 of the work |

Collaborator Contribution | They each did another 1/3. |

Impact | preprint arXiv:1211.3409 |

Start Year | 2011 |

Description | Vortices |

Organisation | University of Tokyo |

Department | Department of Physics |

Country | Japan |

Sector | Academic/University |

PI Contribution | I participated in writing a paper on vortex loop operators with Filippo Passerini and Takuya Okuda. I did 1/3 of the work |

Collaborator Contribution | They each did another 1/3. |

Impact | preprint arXiv:1211.3409 |

Start Year | 2011 |

Description | quark-antiquark |

Organisation | Max Planck Society |

Department | Max Planck Institute for Gravitational Physics |

Country | Germany |

Sector | Academic/University |

PI Contribution | I've been working with a member of the Max Planck Institute in Golm on a project to study the quark antiquark potential in gauge theory and string theory. |

Collaborator Contribution | We are collaborating on a project to be completed soon. |

Impact | paper: JHEP 1106 (2011) 131 and proceeding: Fortsch.Phys. 60 (2012) 1019-1025 |

Start Year | 2010 |

Description | CERN Summer School |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Professional Practitioners |

Results and Impact | I gave a lecture on string theory to approximately 150 students at the CERN Summer school. These are primarily engineers and experimental physicists who are not trained in theoretical physics. there was great interest shown in string theory with the students looking for further information. |

Year(s) Of Engagement Activity | 2012,2013,2014 |

Description | Public Lecture at IOP Edinburgh |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | Yes |

Type Of Presentation | Keynote/Invited Speaker |

Geographic Reach | Regional |

Primary Audience | Public/other audiences |

Results and Impact | 100 people attended the talk and engaged in questions and discussions. None that I am aware of. |

Year(s) Of Engagement Activity | 2012 |

Description | School Visit (George Marshall) |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Schools |

Results and Impact | I gave a presentation to 30 school children about Particle Physics and Cosmology I was invited to visit the school and was featured on their magazine. The students were very interested. |

Year(s) Of Engagement Activity | 2012,2013 |

Description | Student Colloquium |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | Local |

Primary Audience | Public/other audiences |

Results and Impact | I gave a public talk to the mathematics students at King's about the Higgs Boson. This stimulated discussion and an interest in further study of particle physics. The students were interested and wanted to learn more. |

Year(s) Of Engagement Activity | 2013 |

Description | TV |

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 | Was invited to meet with a child prodigy and be filmed for a channel 4 tv show. There was a tv documentary made about a young boy with a deep interest in Physics and mathematics. |

Year(s) Of Engagement Activity | 2014 |

Description | WB |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Policymakers/politicians |

Results and Impact | I gave a talk to the World Bank Office in Ankara Turkey on the Higgs Bosoon I tried to explain how important science and in particular fundamental science is important for the intellectual capitol of a country and urged the audience to encourage more fundamental science with the government counterparts. |

Year(s) Of Engagement Activity | 2014 |