## Contact

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

Applicant | Beisert Niklas |
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Number | 137616 |

Funding scheme | Project funding (Div. I-III) |

Research institution | Institut für Theoretische Physik ETH Zürich |

Institution of higher education | ETH Zurich - ETHZ |

Main discipline | Theoretical Physics |

Start/End | 01.10.2011 - 30.09.2014 |

Approved amount | 556'979.00 |

Quantum Algebra; Quantum Field Theory; Integrable Models; Spin Chains; Gauge Theory; String Theory; AdS/CFT Correspondence

Lead |
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Lay summary |

Our present fundamental understanding of nature at the smallest scales – elementary particles and their interactions – is rooted in Quantum Field Theory. The framework of QFT offers a broad array of methods to construct models and derive the quantities one is interested in. However, many important questions remain unanswered, such as the formulation of a viable theory of Quantum Gravity or performing calculations in the regime of strong interactions. In this context, the so-called AdS/CFT string/gauge duality is an intriguing proposal which has far-reaching consequences for QFT and which addresses several of its open problems. It claims the exact equivalence of certain QFT gauge theory models with particular string theories. The gauge theories on the one side are technically similar to the Standard Model of Particle Physics, albeit they have a different set of particles and interactions. String theories on the other side always contain gravitational interactions. Hence, in brief, an innocently-looking QFT model may actually be equivalent to a model of Quantum Gravity. What obscures this relationship is that it is of a strong/weak kind: It relates the accessible regime of weak interactions in one model to the inaccessible strongly interacting regime in the other model. In other words, the AdS/CFT duality makes strong and important predictions, but they are equally hard to confirm in practice. During the past couple of years, tremendous and rapid progress has been made in exploring a particular AdS/CFT pair of models. Most importantly, exact results in the strongly interacting regime have become available. Moreover the efforts in computation are much lower than the standard Feynman graph techniques for the weakly interacting regime. These results not only support the validity of the AdS/CFT duality. They also give novel insights into the behaviour of QFT at strong coupling. The key to progress lies in the seeming integrability of these models. Here, integrability can be understood as a large amount of hidden symmetries that effectively determines the dynamics of the model at all interaction stregths. In this project we will establish and develop further the mathematical structures of Quantum Algebra that underlie the above described results. This will be an important step towards proving integrability, the applied methods, results at finite coupling, and consequently a part of the AdS/CFT correspondence. Interestingly, there are also applications to condensed matter theory: The very same structures also appear in celebrated models of magnetism and electron transport: the Heisenberg spin chain and the one-dimensional Hubbard model. |

Direct link to Lay Summary | Last update: 21.02.2013 |

Name | Institute |
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Publication |
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Maximally extended sl(2|2) as a quantum double |

Fusion for the one-dimensional Hubbard model |

Integrability of Smooth Wilson Loops in N=4 Superspace |

Local contributions to factorized soft graviton theorems at loop level |

Smooth Wilson Loops in N=4 Non-Chiral Superspace |

The exact spectrum and mirror duality of the (AdS_5 × S^5)_η superstring |

A dictionary between R-operators, on-shell graphs and Yangian algebras |

Constraining subleading soft gluon and graviton theorems |

Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory |

On Yangian-invariant regularization of deformed on-shell diagrams in N=4 super-Yang-Mills theory |

The RTT realization for the deformed gl (2|2) Yangian |

Wilson loops in N=6 superspace for ABJM theory |

Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane |

Integrable Deformations of the XXZ Spin Chain |

The Quantum Deformed Mirror TBA I |

The Quantum Deformed Mirror TBA II |

Twistors, Harmonics and Holomorphic Chern-Simons |

Co-ideal quantum affine algebra and boundary scattering of the deformed Hubbard chain |

Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory |

Construction of Lax Connections by Exponentiation |

Null polygonal Wilson loops in full N=4 superspace |

On the Geometry of null polygons in full N=4 superspace |

Secret Symmetries in AdS/CFT |

The quantum affine origin of the AdS/CFT secret symmetry |

The spectral problem for strings on twisted AdS(5) x S-5 |

Group / person | Country |
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Types of collaboration |
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Max-Planck-Institut für Gravitationsphysik | Germany (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Humboldt Universität zu Berlin | Germany (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Utrecht University | Netherlands (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Vilnius University | Lithuania (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

University of Sydney | Australia (Oceania) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Uppsala University | Sweden (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

University of Surrey | Great Britain and Northern Ireland (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Niels Bohr Institute | Denmark (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

The University of York | Great Britain and Northern Ireland (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Title | Type of contribution | Title of article or contribution | Date | Place | Persons involved |
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SwissMAP general meeting | Talk given at a conference | Yangian Symmetry in the AdS/CFT Correspondence | 28.08.2014 | Leysin, Switzerland | Beisert Niklas; |

New Trends in Quantum Integrability | Talk given at a conference | A quantum double for the centrally extended sl(2|2) | 18.08.2014 | Surrey, Great Britain and Northern Ireland | De Leuuw Marius; |

Institut d'Été: Strings, Matrices, Integrability | Talk given at a conference | Metastable Spinning Strings | 18.08.2014 | Paris, France | Beisert Niklas; |

PSI Summer School: More than Higgs - Effective Theories for Particle Physics | Talk given at a conference | String Theory | 18.08.2014 | Zuoz, Switzerland | Beisert Niklas; |

Quantum Integrability, Conformal Field Theory and Topological Quantum Computation | Talk given at a conference | RTT Realisation of the Yangian for the Hubbard Chain | 24.03.2014 | Natal, Brazil | Beisert Niklas; |

Physics and Mathematics of Deformed Scattering Amplitudes | Talk given at a conference | On Yangian Symmetry of Deformed Scattering Amplitudes | 24.10.2013 | Stony Brook, United States of America | Beisert Niklas; |

The String Theory Universe | Talk given at a conference | Yangian Symmetry in the AdS/CFT Correspondence | 02.09.2013 | Bern, Switzerland | Beisert Niklas; |

Integrability in Gauge and String Theory 2013 | Talk given at a conference | RTT realization of the AdS/CFT Yangian | 19.08.2013 | Utrecht, Netherlands | De Leuuw Marius; |

The 8th Symposium on Quantum Theory and Symmetries | Talk given at a conference | Yangian Symmetry in the AdS/CFT Correspondence | 05.08.2013 | Mexico City, Mexico | Beisert Niklas; |

Amplitudes, Strings and Branes | Talk given at a conference | On Yangian Symmetry of Scattering Amplitudes | 15.07.2013 | Geneva, Switzerland | Beisert Niklas; |

Euler Symposium on Theoretical and Mathematical Physics | Talk given at a conference | RTT Realisation of the Yangian for the Hubbard Chain | 12.07.2013 | St Petersburg, Russia | Beisert Niklas; |

Recent Advances in Quantum Integrable Systems 12 | Talk given at a conference | Quantum deformations in AdS/CFT | 10.09.2012 | Angers, France | De Leuuw Marius; |

Scattering Amplitudes: from QCD to maximally supersymmetric Yang-Mills theory and back | Talk given at a conference | Scattering in N = 6 Chern–Simons Theory and Superconformal Symmetry | 16.07.2012 | Trento, Italy | Beisert Niklas; |

Representation Theory in Mathematics and Physics | Talk given at a conference | Quantum Algebra from the AdS/CFT duality | 04.06.2012 | Zurich, Switzerland | Beisert Niklas; |

Maths of String and Gauge Theory | Talk given at a conference | Null Polygonal Wilson Loops in Full N = 4 Superspace | 03.05.2012 | London, Great Britain and Northern Ireland | Beisert Niklas; |

N=4 Super Yang-Mills Theory, 35 Years After | Talk given at a conference | Null Polygonal Wilson Loops in Full N = 4 Superspace | 29.03.2012 | Pasadena, CA, United States of America | Beisert Niklas; |

Amplitudes 2012 | Talk given at a conference | Null Polygonal Wilson Loops in Full N = 4 Superspace | 05.03.2012 | Hamburg, Germany | Beisert Niklas; |

Integrable lattice models and quantum field theories | Talk given at a conference | A quantum affine algebra for the deformed Hubbard chai | 17.02.2012 | Wuppertal, Germany | Beisert Niklas; |

Exact Results in Gauge-String Dualities | Talk given at a conference | Null Polygonal Wilson Loops in Full N=4 Superspace | 23.01.2012 | Stockholm, Sweden | Beisert Niklas; |

Title | Date | Place |
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Recent Developments in String Theory | 21.07.2014 | Ascona, Switzerland |

Integrability in Gauge and String Theory 2013 | 19.08.2013 | Utrecht, Netherlands |

Amplitudes 2013 | 29.04.2013 | Ringberg, Germany |

Integrability in Gauge and String Theory 2012 | 20.08.2012 | Zurich, Switzerland |

Communication | Title | Media | Place | Year |
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Talks/events/exhibitions | Teilchenphysik, Stringtheorie und Magnetismus | German-speaking Switzerland | 2012 |

Title | Year |
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New Horizons in Physics Prize | 2013 |

Participation at the 25th Solvay Conference | 2011 |

Our present fundamental understanding of nature at the smallest scales -- elementary particles and their interactions -- is rooted in Quantum Field Theory. The framework of QFT offers a broad array of methods to construct models and derive the observables one is interested in. However, many important questions remain unanswered, such as the formulation of a viable theory of quantum gravity or the problem of gaining access to the non-perturbative regime, just to name two.During the past couple of years, tremendous and rapid progress has been made in exploring a particular QFT, namely N=4 Supersymmetric Yang-Mills theory in the planar limit. We have gained a good understanding of its spectrum of local operators, its S-matrix as well as other observables. These results go far beyond what is otherwise accessible by perturbative methods such as Feynman diagrams. Most importantly, some calculations at finite coupling have become feasible. Although these results are merely based on a series of assumptions, they have been verified by elaborate perturbative calculations. They are also in full agreement with predictions from the AdS/CFT string/gauge correspondence which relates the strong coupling regime to weakly coupled string theory on the AdS5xS5 background. The key to progress lies in the seeming integrability of the planar sector of N=4 SYM, which can be understood in terms of a large amount of hidden symmetries that effectively determine the dynamics of the model, even at finite coupling. Within the proposed project I would like to establish and develop further the mathematical structures that underlie the above described results. This will be an important step towards proving for integrability, the applied methods, results at finite coupling, and consequently a part of the AdS/CFT correspondence. A suitable mathematical framework for integrable models is quantum algebra, more precisely quantum affine and related algebras. In the present case they are based on the Lie superalgebras psu(2|2) and psu(2,2|4). In particular, the former possesses some remarkable exceptional features that let the associated quantum algebra escape the established framework. Curiously, here one finds a connection to another exceptional physical model in the very different context of strongly correlated electrons: Integrability of the one-dimensional Hubbard model is based on the very same algebraic structures. Research in the project will focus on the investigation of these particular quantum algebras, their formulation and the application to physical models.

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

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