Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM

Abstract

There is a growing amount of evidence that QCD (and four-dimensional gauge theories in general) possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. In this review we consider the scale dependence of local gauge invariant operators and high-energy (Regge) behavior of scattering amplitudes to explain that the effective QCD dynamics in both cases is described by completely integrable systems that prove to be related to the celebrated Heisenberg spin chain and its generalizations.

28 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated

References in corpus (4)

• Conformal properties of four-gluon planar amplitudes and Wilson loops
• Logarithmic scaling in gauge/string correspondence
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Towards Baxter equation in supersymmetric Yang-Mills theories

Cited by in corpus (20)

• Exact Bremsstrahlung and Effective Couplings
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• The Exact Effective Couplings of 4D N=2 gauge theories
• Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills
• Reggeon Field Theory for Large Pomeron Loops
• Integrability in N=2 superconformal gauge theories
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
• QCD Reggeon Calculus From KLWMIJ/JIMWLK Evolution: Vertices, Reggeization and All
• On the Integrability of Planar N=2 Superconformal Gauge Theories
• The Heisenberg XX spin chain and low-energy QCD
• The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector
• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
• The Complete One-loop Spin Chain of N =1 SQCD
• Free quantum fields in 4D and Calabi-Yau spaces
• A pedagogical introduction to quantum integrability, with a view towards theoretical high-energy physics
• The dual string sigma-model of the SU_q(3) sector
• On the massless modes of the AdS3/CFT2 integrable systems
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Strings from large charged fields