Quantum Algebra; Quantum Field Theory; Integrable Models; Spin Chains; Gauge Theory; String Theory; AdS/CFT Correspondence
Beisert Niklas, de Leeuw Marius, Hecht Reimar (2016), Maximally extended sl(2|2) as a quantum double, in J. Phys. A
, 43, 434005.
Beisert Niklas, de Leeuw Marius, Nag Panchali (2015), Fusion for the one-dimensional Hubbard model, in J. Phys. A
, 48, 324002.
Beisert Niklas, Müller Dennis, Plefka Jan, Vergu Cristian (2015), Integrability of Smooth Wilson Loops in N=4 Superspace, in JHEP
, 1512, 141.
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.
Beisert Niklas, Müller Dennis, Plefka Jan, Vergu Cristian (2015), Smooth Wilson Loops in N=4 Non-Chiral Superspace, in JHEP
, 1512, 140.
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.
Broedel Johannes, De Leeuw Marius, Rosso Matteo (2014), A dictionary between R-operators, on-shell graphs and Yangian algebras, in JHEP
, 1406, 170.
Broedel Johannes, de Leeuw Marius, Plefka Jan, Rosso Matteo (2014), Constraining subleading soft gluon and graviton theorems, in Physical Review D
, 90, 065024.
Broedel Johannes, de Leeuw Marius, Rosso Matteo (2014), Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory, in JHEP
, 2014(11), 091.
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.
Beisert Niklas, de Leeuw Marius (2014), The RTT realization for the deformed gl (2|2) Yangian, in Journal of Physics A
, 47(30), 305201.
Rosso Matteo, Vergu Cristian (2014), Wilson loops in N=6 superspace for ABJM theory, in JHEP
, 1406, 176.
de Leeuw Marius, Regelskis Vidas (2013), Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane, in JHEP
, 1303, 030.
Beisert Niklas, Fiévet Lucas, de Leeuw Marius, Loebbert Florian (2013), Integrable Deformations of the XXZ Spin Chain, in J. Stat. Mech.
, 13, P09028.
Arutyunov Gleb, de Leeuw Marius, van Tongeren Stijn J. (2013), The Quantum Deformed Mirror TBA I, in JHEP
, 1210, 090.
Arutyunov Gleb, de Leeuw Marius, van Tongeren Stijn J. (2013), The Quantum Deformed Mirror TBA II, in JHEP
, 1302, 012.
Schwab Burkhard U. W., Vergu Cristian (2013), Twistors, Harmonics and Holomorphic Chern-Simons, in JHEP
, 1303, 046.
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--.
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.
Beisert Niklas, Luecker Florian (2012), Construction of Lax Connections by Exponentiation, in J.Math.Phys.
, 53, 122304.
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--.
Beisert Niklas, Vergu Cristian (2012), On the Geometry of null polygons in full N=4 superspace, in Physical Review D
, 86(2), 026006--.
de Leeuw Marius, Matsumoto Takuya, Moriyama Sanefumi, Regelskis Vidas, Torrielli Alessandro (2012), Secret Symmetries in AdS/CFT, in Physica Scripta
, 02, 028502--.
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--.
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.
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.