Project

Back to overview

Algebraic Foundations of Integrability in the Planar Gauge/String Duality

Applicant Beisert Niklas
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
Show all

Keywords (7)

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

Lay Summary (English)

Lead
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

Responsible applicant and co-applicants

Employees

Publications

Publication
Maximally extended sl(2|2) as a quantum double
Beisert Niklas, de Leeuw Marius, Hecht Reimar (2016), Maximally extended sl(2|2) as a quantum double, in J. Phys. A, 43, 434005.
Fusion for the one-dimensional Hubbard model
Beisert Niklas, de Leeuw Marius, Nag Panchali (2015), Fusion for the one-dimensional Hubbard model, in J. Phys. A, 48, 324002.
Integrability of Smooth Wilson Loops in N=4 Superspace
Beisert Niklas, Müller Dennis, Plefka Jan, Vergu Cristian (2015), Integrability of Smooth Wilson Loops in N=4 Superspace, in JHEP, 1512, 141.
Local contributions to factorized soft graviton theorems at loop level
Broedel Johannes, de Leeuw Marius, Plefka Jan, Rosso Matteo (2015), Local contributions to factorized soft graviton theorems at loop level, in Physics Letters B, 746, 293-299.
Smooth Wilson Loops in N=4 Non-Chiral Superspace
Beisert Niklas, Müller Dennis, Plefka Jan, Vergu Cristian (2015), Smooth Wilson Loops in N=4 Non-Chiral Superspace, in JHEP, 1512, 140.
The exact spectrum and mirror duality of the (AdS_5 × S^5)_η superstring
Arutyunov Gleb, de Leeuw Marius, van Tongeren Stijn J. (2015), The exact spectrum and mirror duality of the (AdS_5 × S^5)_η superstring, in Theoretical and Mathematical Physics, 182, 23-51.
A dictionary between R-operators, on-shell graphs and Yangian algebras
Broedel Johannes, De Leeuw Marius, Rosso Matteo (2014), A dictionary between R-operators, on-shell graphs and Yangian algebras, in JHEP, 1406, 170.
Constraining subleading soft gluon and graviton theorems
Broedel Johannes, de Leeuw Marius, Plefka Jan, Rosso Matteo (2014), Constraining subleading soft gluon and graviton theorems, in Physical Review D, 90, 065024.
Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
Broedel Johannes, de Leeuw Marius, Rosso Matteo (2014), Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory, in JHEP, 2014(11), 091.
On Yangian-invariant regularization of deformed on-shell diagrams in N=4 super-Yang-Mills theory
Beisert Niklas, Broedel Johannes, Rosso Matteo (2014), On Yangian-invariant regularization of deformed on-shell diagrams in N=4 super-Yang-Mills theory, in Journal of Physics A, 47(36), 365402.
The RTT realization for the deformed gl (2|2) Yangian
Beisert Niklas, de Leeuw Marius (2014), The RTT realization for the deformed gl (2|2) Yangian, in Journal of Physics A, 47(30), 305201.
Wilson loops in N=6 superspace for ABJM theory
Rosso Matteo, Vergu Cristian (2014), Wilson loops in N=6 superspace for ABJM theory, in JHEP, 1406, 176.
Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
de Leeuw Marius, Regelskis Vidas (2013), Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane, in JHEP, 1303, 030.
Integrable Deformations of the XXZ Spin Chain
Beisert Niklas, Fiévet Lucas, de Leeuw Marius, Loebbert Florian (2013), Integrable Deformations of the XXZ Spin Chain, in J. Stat. Mech., 13, P09028.
The Quantum Deformed Mirror TBA I
Arutyunov Gleb, de Leeuw Marius, van Tongeren Stijn J. (2013), The Quantum Deformed Mirror TBA I, in JHEP, 1210, 090.
The Quantum Deformed Mirror TBA II
Arutyunov Gleb, de Leeuw Marius, van Tongeren Stijn J. (2013), The Quantum Deformed Mirror TBA II, in JHEP, 1302, 012.
Twistors, Harmonics and Holomorphic Chern-Simons
Schwab Burkhard U. W., Vergu Cristian (2013), Twistors, Harmonics and Holomorphic Chern-Simons, in JHEP, 1303, 046.
Co-ideal quantum affine algebra and boundary scattering of the deformed Hubbard chain
de Leeuw Marius, Matsumoto Takuya, Regelskis Vidas (2012), Co-ideal quantum affine algebra and boundary scattering of the deformed Hubbard chain, in Journal of Physics A, 45(6), 065205--.
Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
Bargheer Till, Beisert Niklas, Loebbert Florian, McLoughlin Tristan (2012), Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory, in J. Phys. A, 45, 475402.
Construction of Lax Connections by Exponentiation
Beisert Niklas, Luecker Florian (2012), Construction of Lax Connections by Exponentiation, in J.Math.Phys., 53, 122304.
Null polygonal Wilson loops in full N=4 superspace
Beisert Niklas, He Song, Schwab Bukhard U. W., Vergu Cristian (2012), Null polygonal Wilson loops in full N=4 superspace, in Journal of Physics A, Mathematical and theoretical, 45(26), 265402--.
On the Geometry of null polygons in full N=4 superspace
Beisert Niklas, Vergu Cristian (2012), On the Geometry of null polygons in full N=4 superspace, in Physical Review D, 86(2), 026006--.
Secret Symmetries in AdS/CFT
de Leeuw Marius, Matsumoto Takuya, Moriyama Sanefumi, Regelskis Vidas, Torrielli Alessandro (2012), Secret Symmetries in AdS/CFT, in Physica Scripta, 02, 028502--.
The quantum affine origin of the AdS/CFT secret symmetry
Leeuw Marius de, Regelskis Vidas, Torrielli Alessandro (2012), The quantum affine origin of the AdS/CFT secret symmetry, in Journal of Physics A, 45(17), 175202--.
The spectral problem for strings on twisted AdS(5) x S-5
Leeuw Marius de, Tongeren Stijn J. van (2012), The spectral problem for strings on twisted AdS(5) x S-5, in Nuclear Physics B, 860(3), 339-376.

Collaboration

Group / person Country
Types of collaboration
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

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
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;


Self-organised

Title Date Place
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 with the public

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

Awards

Title Year
New Horizons in Physics Prize 2013
Participation at the 25th Solvay Conference 2011

Abstract

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.
-