Nesting and Dressing

Abstract

We compute the anomalous dimensions of field strength operators Tr F^L in N=4 SYM from an asymptotic nested Bethe ansatz to all-loop order. Starting from the exact solution of the one-loop problem at arbitrary L, we derive a single effective integral equation for the thermodynamic limit of these dimensions. We also include the recently proposed phase factor for the S-matrix of the planar AdS/CFT system. The terms in the effective equation corresponding to, respectively, the nesting and the dressing are structurally very similar. This hints at the physical origin of the dressing phase, which we conjecture to arise from the hidden presence of infinitely many auxiliary Bethe roots describing a non-trivial "filled" structure of the theory's BPS vacuum. We finally show that the mechanism for creating effective nesting/dressing kernels is quite generic by also deriving the integral equation for the all-loop dimension of a certain one-loop so(6) singlet state.

38 pages, 2 figures. v2: References and appendix discussing the emulation of the dressing phase added

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• A semi-classical limit of the gauge/string correspondence
• 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
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• Giant Magnons
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• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Baryon Distribution Amplitudes in QCD
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Cited by in corpus (11)

• Wrapping interactions at strong coupling -- the giant magnon
• A Generalized Scaling Function for AdS/CFT
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Analytic three-loop Solutions for N=4 SYM Twist Operators
• Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
• From nesting to dressing
• The Yangian of sl(n|m) and the universal R-matrix
• Deviation from Alday-Maldacena Duality For Wavy Circle
• QCD-like properties for anomalous dimensions in N=4 SYM
• Giant Spinons