Spin bit models from non-planar N=4 SYM

Abstract

We study spin models underlying the non-planar dynamics of $\mathcal{N}=4$ SYM gauge theory. In particular, we derive the non-local spin chain Hamiltonian generating dilatations in the gauge theory at leading order in $g_{\mathrm{YM}}^{2}N$ but exact in $\frac{1}{N}$. States in the spin chain are characterized by a spin-configuration and a linking variable describing how sites in the chain are connected. Joining and splitting of string/traces are mimicked by a twist operator acting on the linking variable. The results are applied to a systematic study of non-planar anomalous dimensions and operator mixing in $\mathcal{N}=4$ SYM. Intriguingly, we identify a sequence of SYM operators for which corrections to the one-loop anomalous dimensions stop at the first $\frac{1}{N}$ non-planar order.

22 pages, 2 figures, some typos corrected in eqs. (2.6), (2.8), (2.11), (2.14)

References in corpus (17)

• Spinning strings in AdS_5 x S^5 and integrable systems
• On higher spins and the tensionless limit of String Theory
• Matching Higher Conserved Charges for Strings and Spins
• Precision Spectroscopy of AdS/CFT
• From Free Fields to $AdS$
• On lightcone string field theory from Super Yang-Mills and holography
• Higher Spin Symmetry and N=4 SYM
• On the Frame-Like Formulation of Mixed-Symmetry Massless Fields in (A)dS(d)
• From Free Fields to $AdS$ -- III
• Lectures on the Plane-Wave String/Gauge Theory Duality
• Massive totally symmetric fields in AdS(d)
• On the spectrum of AdS/CFT beyond supergravity
• On the covariant quantization of tensionless bosonic strings in AdS spacetime
• String bits in small radius AdS and weakly coupled N=4 Super Yang-Mills Theory: I
• Surprises from the Resolution of Operator Mixing in N = 4 SYM
• Light-Cone String Field Theory in a Plane Wave Background
• On the dynamics of BMN operators of finite size and the model of string bits

Cited by in corpus (31)

• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• Higher Spin Symmetry and N=4 SYM
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• SL(2) spin chain and spinning strings on AdS_5xS^5
• N=4 Superconformal Characters and Partition Functions
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• From counting to construction of BPS states in N=4 SYM
• Splitting spinning strings in AdS/CFT
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Permutations and the Loop
• Non-planar ABJM Theory and Integrability
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Quasilocality of joining/splitting strings from coherent states
• Cut-and-join operators and N=4 super Yang-Mills
• Quarter BPS classified by Brauer algebra
• Three-point correlators of twist-2 operators in N=4 SYM at Born approximation
• Superstring sigma models from spin chains: the SU(1,1|1) case
• On the boundary gauge dual of closed tensionless free strings in AdS
• Sigma model from SU(1,1|2) spin chain
• On matrix models for anomalous dimensions of super Yang-Mills theory
• Spin bits at two loops
• Refined Counting of Necklaces in One-loop $\mathcal{N}=4$ SYM
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• Statistical mechanics for dilatations in N=4 super Yang--Mills theory
• On dilatation operator for a renormalizable theory
• Non-planar spin bits beyond two loops
• Non-planar operator mixing by Brauer representations
• Random walks in N = 4 Super Yang-Mills
• Mass-Gaps and Spin Chains for (Super) Membranes
• Dilatation Operator and Space-time Geometry
• Matrix at slow roll: Nonrelativistic and Perturbative