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.

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.

Publications

10 25 50

 
Description 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 Academic/University
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 European Union (EU)
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 Learned Society
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 Learned Society
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 European Union (EU) 
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 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 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 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 Public 
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