One-Loop QCD Spin Chain and its Spectrum

Abstract

We study the renormalization of gauge invariant operators in large Nc QCD. We compute the complete matrix of anomalous dimensions to leading order in the 't Hooft coupling and study its eigenvalues. Thinking of the mixing matrix as the Hamiltonian of a generalized spin chain we find a large integrable sector consisting of purely gluonic operators constructed with self-dual field strengths and an arbitrary number of derivatives. This sector contains the true ground state of the spin chain and all the gapless excitations above it. The ground state is essentially the anti-ferromagnetic ground state of a XXX1 spin chain and the excitations carry either a chiral spin quantum number with relativistic dispersion relation or an anti-chiral one with non-relativistic dispersion relation.

54 pages, v2: minor changes, references added

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• Exact Bremsstrahlung and Effective Couplings
• Renormalization of Twist-Four Operators in QCD
• 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
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• Anomalous dimensions of potential top-partners
• Decoupling limits of N=4 super Yang-Mills on R x S^3
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory
• Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM
• Spiky Strings and Spin Chains
• The Spectrum of Yang Mills on a Sphere
• On the Integrability of Planar N=2 Superconformal Gauge Theories
• Slow-string limit and "antiferromagnetic" state in AdS/CFT
• The nested SU(N) off-shell Bethe ansatz and exact form factors
• Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains
• Confining Strings, Infinite Statistics and Integrability
• Two loop partition function for large N pure Yang-Mills theory on a small three-sphere
• Semiclassical rigid strings with two spins in AdS_5
• Integrable Spin Chains on the Conformal Moose
• Nesting and Dressing
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• Anomalous dimensions of finite size field strength operators in N=4 SYM
• $n$-point correlators of twist-$2$ operators in $SU(N)$ Yang-Mills theory to the lowest perturbative order
• The dual string sigma-model of the SU_q(3) sector
• Higher Charges in Dynamical Spin Chains for SYM Theory
• OPE in planar QCD from integrability
• UV asymptotics of $n$-point correlators of twist-$2$ operators in SU($N$) Yang-Mills theory
• QCD-like properties for anomalous dimensions in N=4 SYM
• Heavy hadron spectra from spin chains and strings
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
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• From QCD Strings to WZW
• Nonresonant renormalization scheme for twist-$2$ operators in SU($N$) Yang-Mills theory
• The QCD spin chain S matrix
• Giant Gravitons Intersecting at Angles from Integrable Spin Chains
• Glueballs propagators in large-N YM
• String Solutions in General Backgrounds