New Integrable Structures in Large-N QCD

Abstract

We study the anomalous dimensions of single trace operators composed of field strengths $F_{\mu \nu }$ in large-N QCD. The matrix of anomalous dimensions is the Hamiltonian of a compact spin chain with two spin one representations at each vertex corresponding to the selfdual and anti-selfdual components of $F_{\mu \nu }$. Due to the special form of the interaction it is possible to study separately renormalization of purely selfdual components. In this sector the Hamiltonian is integrable and can be exactly solved by Bethe ansatz. Its continuum limit is described by the level two SU(2) WZW model.

12 pages; V2: ref. added, V3: refs. added, explicit expression for the spin ladder and other text improvements

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• Integrability in QCD and beyond
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• Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator
• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• One-Loop QCD Spin Chain and its Spectrum
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• Pulsating Strings on AdS_5 x S^5
• Spin chain sigma models with fermions
• The Bethe Ansatz for Z_S Orbifolds of N=4 Super Yang-Mills Theory
• Integrability in N=2 superconformal gauge theories
• Semiclassical circular strings in AdS_5 and "long" gauge field strength operators
• On the finite size corrections of anti-ferromagnetic anomalous dimensions in $\mathcal{N}=4$ SYM
• Decoupling limits of N=4 super Yang-Mills on R x S^3
• Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory
• Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM
• N=2 Super Yang-Mills and the XXZ spin chain
• Glueball and meson propagators of any spin in large-N QCD
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part II: $0<\mathcal{N}<4$ super Yang-Mills
• Slow-string limit and "antiferromagnetic" state in AdS/CFT
• Exactly solvable models in atomic and molecular physics
• Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models
• Confining Strings, Infinite Statistics and Integrability
• Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions
• Pulsating Strings With Angular Momenta
• Semiclassical rigid strings with two spins in AdS_5
• Integrability and unitarity
• Nesting and Dressing
• Sum rules for higher twist sl(2)operators in N=4 SYM
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• Yang-Mills mass gap, Floer homology, glueball spectrum, and conformal window in large-N QCD
• Gauge Theories as String Theories: the First Results
• OPE in planar QCD from integrability
• Higher Charges in Dynamical Spin Chains for SYM Theory
• The dual string sigma-model of the SU_q(3) sector
• QCD-like properties for anomalous dimensions in N=4 SYM
• Finite size effects and 2-string deviations in the spin-1 XXZ chains
• On novel string theories from 4d gauge theories
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• From QCD Strings to WZW
• Mass-Gaps and Spin Chains for (Super) Membranes
• An asymptotic solution of large-$N$ $QCD$, and of large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$
• The QCD spin chain S matrix
• Renormalization group flow of reduced string actions
• Glueballs propagators in large-N YM