A relation between approaches to integrability in superconformal Yang-Mills theory

By L. Dolan, C. Nappi, E. Witten. 2003

274 citations recorded by the source corpus.

We make contact between the infinite-dimensional non-local symmetry of the type-IIB superstring on AdS5 × S5 and a non-abelian infinite-dimensional symmetry algebra for the weakly coupled superconformal gauge theory. We explain why the planar limit of the one-loop dilatation operator is the hamiltonian of a spin chain, and show that it commutes with the g2N = 0 limit of the non-abelian charges.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bd94496f7b76c0334898ce28354552b344e15f3f

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Citations in the corpus

Wrapping interactions and a new source of corrections to the spin-chain/string duality (2005, background): “1 Introduction The discovery of integrable structures underlying planar N = 4 SYM [1, 2, 3, 4] as well as classical string theory on AdS5 × S(5) [5, 6, 7, 8, 9, 10, 11] has opened up new avenues for testing the AdS/CFT correspondence [12].”
SPINNING STRINGS AND AdS/CFT DUALITY (2003, background): “18) may not be, and thus Q(2) may not be welldefined (see also related comments in [46, 47]).”
Algebraic Curve for the SO(6) Sector of AdS/CFT (2004, unknown): “(2.42)”
Dual superconformal invariance, momentum twistors and Grassmannians (2009, background): “A systematic exploitation of both dual superconformal invariance and the BCFW recursion relations [7,8] then led to an explicit solution [6] for all N = 4 SYM trees.”
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, background): “This similarity allowed the authors of [116] to promote the Yangian structure from string theory to gauge theory.”
INTRODUCTION TO YANGIAN SYMMETRY IN INTEGRABLE FIELD THEORY (2004, background): “iversal ebveloping algebras now in common use’ [3], and perhaps that is now becoming more widely believed. Certainly Yangians are making an appearance on both sides of the gauge/string correspondence [4, 5]. The intention of these lectures is to give a pedagogical introduction for physicists. They c”
Spinning strings in AdS(5) x S**5: New integrable system relations (2003, background): “While recent papers [9, 10, 11, 25] shed some light on how the integrability of the AdS5×S(5) string theory is related to that of the planar SYM theory, many details are missing.”
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “A real breakthrough in this respect is the discovery of integrability on both sides of the duality [2, 3, 4, 5, 6, 7].”
Symmetries of Tree-level Scattering Amplitudes in N = 6 Superconformal Chern{Simons Theory (2010, unknown): “[32, 23].”
The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, background): “One of the most fascinating discoveries in recent years was the unravelling of integrable structures in planar N = 4 SYM [1, 2, 3, 4] and in superstring theory on AdS5 × S(5) [5, 6, 7, 8, 9, 10, 11].”
Four loop twist two, BFKL, wrapping and strings (2008, background): “The integrable structures which appear both on the gauge theory side [1, 2, 3, 4, 5] and the string theory side [6] of the AdS/CFT correspondence [7] give hope to find the full spectrum of both theories.”
Matching Higher Conserved Charges for Strings and Spins (2003, background): “3See[16]forsom eideasbased on relation between thediscretized Neum ann system and theXYZ spin chain. counterparthasbeen recently discussed from theviewpointofnonabelian (nonlocal) sym m etriesgeneratedbyYangians[17,18,19](seealso[20]forfurtherdevelopm ents).”
Classical/quantum integrability in non-compact sector of AdS/CFT (2004, background): “The Bethe ansatz solution of this model and related spin systems was extremely useful in comparing anomalous dimensions of local operators in SYM [16, 17, 18] to the energies of classical string solitons in AdS5 × S5 [19, 20, 21, 22].”
Yang-Mills duals for semiclassical strings on AdS5 × S5 (2003, background): “In [42], some progress was made toward relating the integrability of the oneloop dilatation operator and the non-local symmetries in the sigma model.”