Aspects of Integrability in N =4 SYM

Abstract

Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this review, we highlight some connections between superconformal four dimensional Yang-Mills theory and various integrable systems. In particular, we focus on the role of Yangian symmetries in studying the gauge theory dual of closed string excitations. We also briefly review how the gauge theory connects to Calogero models and open quantum spin chains through the study of the gauge theory duals of D3 branes and open strings ending on them. This invited review, written for Modern Physics Letters-A, is based on a seminar given at the Institute of Advanced Study, Princeton.

Invited brief review for Mod. Phys. Lett. A based on a talk at I.A.S, Princeton

References in corpus (19)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Transcendentality and Crossing
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Planar N=4 Gauge Theory and the Hubbard Model
• Integrable open spin chains from giant gravitons
• On the Hopf algebra structure of the AdS/CFT S-matrix
• An Introduction to Yangian Symmetries
• Yangian Symmetries of Matrix Models and Spin Chains: The Dilatation Operator of $\mathcal{N}$$=4$ SYM
• Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
• A Yangian Double for the AdS/CFT Classical r-matrix
• The S-Matrix of AdS/CFT and Yangian Symmetry
• Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• $gl(n|m)$ color Calogero-Sutherland models and Super Yangian Algebra
• Introduction to Yangian in Physics

Cited by in corpus (2)

• Open Perturbatively Long-Range Integrable gl(N) Spin Chains
• Yangians in Deformed Super Yang-Mills Theories