The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory

Abstract

We continue the analysis of hep-th/0303060 in the one-loop sector and present the complete psu(2,2|4) dilatation operator of N=4 Super Yang-Mills theory. This operator generates the matrix of one-loop anomalous dimensions for all local operators in the theory. Using an oscillator representation we show how to apply the dilatation generator to a generic state. By way of example, we determine the planar anomalous dimensions of all operators up to and including dimension 5.5, where we also find some evidence for integrability. Finally, we investigate a number of subsectors of N=4 SYM in which the dilatation operator simplifies. Among these we find the previously considered so(6) and su(2) subsectors, a su(2|4) subsector isomorphic to the BMN matrix model at one-loop, a u(2|3) supersymmetric subsector of nearly eighth-BPS states and, last but not least, a non-compact sl(2) subsector whose dilatation operator lifts uniquely to the full theory.

39 pages, 1 figure, v2,v3: typos, minor corrections and references added, v4: minor corrections, accepted for publication in Nucl. Phys. B, v5: intermediate results (B.16/B.18) in Appendix B corrected, thanks to Pedro Liendo for pointing out my mistake

References in corpus (16)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Stringing Spins and Spinning Strings
• Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors
• Anomalous dimensions of Wilson operators in N=4 SYM theory
• Gauge/string duality for QCD conformal operators
• On stringy AdS_5 x S^5 and higher spin holography
• BMN Gauge Theory as a Quantum Mechanical System
• Plane-wave Matrix Theory from N=4 Super Yang-Mills on RxS^3
• On the spectrum of AdS/CFT beyond supergravity
• Systematics of Quarter BPS operators in N=4 SYM
• Conformal Dimensions of Two-Derivative BMN Operators
• Note on Plane Wave Quantum Mechanics
• BMN operators with vector impurities, Z_2 symmetry and pp-waves

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