# 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.

### Publications

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Alfimov M (2018) BFKL spectrum of N $$\mathcal{N}$$ = 4: non-zero conformal spin in Journal of High Energy Physics

Bagger J (2013) Multiple membranes in M-theory in Physics Reports

Beisert N (2011) Review of AdS/CFT Integrability: An Overview in Letters in Mathematical Physics

Bergshoeff E (2008) Dual gravity and matter in General Relativity and Gravitation

Bergshoeff E (2010) D-brane Wess-Zumino terms and U-duality in Journal of High Energy Physics

Bergshoeff E (2010) IIA/IIB supergravity and ten-forms in Journal of High Energy Physics

Bombardelli D (2017) The full Quantum Spectral Curve for AdS4/CFT3 in Journal of High Energy Physics

Bourdier J (2014) Holographic RG flows and nearly-marginal operators in Classical and Quantum Gravity

Braun A (2014) Hypercharge flux in F-theory and the stable Sen limit in Journal of High Energy Physics

Braun A (2014) The fate of U(1)'s at strong coupling in F-theory in Journal of High Energy Physics

Description 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Country Japan
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
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
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 Non-Kahler heterotic rotations
Organisation University of Oxford
Department Mathematical Institute Oxford
Country United Kingdom
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
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
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

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