The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
By N. Beisert. 2003
536 citations recorded by the source corpus.
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 YangMills 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.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/5d38c410a7fe10226908c71382d9dc63accba047
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Citations in the corpus
- Five-loop anomalous dimension of twist-two operators (2009, background): “symptotically integrable. In the groundbreaking paper [10] the one-loop integrability of the dilatation operator in certain subsectors of the gauge side of the correspondence was discovered. Later on [11], the complete one-loop dilatation operator and the one-loop Bethe equations were written down i”
- The su(2|3) dynamic spin chain (2003, methodology): “Quite naturally the complete one-loop planar dilatation generator of this theory [7] corresponds to an integrable super spin chain with full psu(2, 2|4) symmetry [8] (for literature on super spin chains, c.”
- Integrable Hamiltonian for Classical Strings on AdS5 x S5 (2004, background): “This was generalized to the complete dilatation operator in [9] and, the integrability, very likely, holds at higher loops as well [10].”
- The Algebraic Curve of Classical Superstrings on AdS5×S5 (2005, unknown): “A. 7In fact, any E = −ET with εαβγδEαβEγδ 6= 0 would suffice and one could as well pick distinct matrices E for E1 and E2.”
- Algebraic Curve for the SO(6) Sector of AdS/CFT (2004, unknown): “ar X ∗Membre de l’Institut Universitaire de France”
- Planar N=4 Gauge Theory and the Inozemtsev Long Range Spin Chain (2004, background): “A unified one-loop treatment of all conformal operators in the N = 4 theory was developed in [8], and shown to yield an integrable PSU(2, 2|4) super spin chain [9], as well as its corresponding Bethe ansatz.”
- Diagonal free field matrix correlators, global symmetries and giant gravitons (2008, methodology): “y derivatives allows a reconstruction of the spacetime dependence. 2.1 Oscillator construction The oscillator representation allows an elegant method of constructing primary fields in the SL(2) sector [26, 27]. By using this representation to find the Clebsch-Gordan coefficients associated with the SL(2”
- The N=4 SYM Integrable Super Spin Chain (2003, background): “It is believed th model is exactly conformally invariant at the quantum level [2] and thus a non-t example (as opposed to free massless field theory) of af ur-dimensional conformal field E-mail addresses: nbeisert@aei.mpg.de (N. Beisert), matthias@aei.mpg.de (M. Staudacher).”
- Yang-Mills duals for semiclassical strings on AdS5 × S5 (2003, background): “More recently, a program has begun comparing the spectrum of semiclassical string configurations [7,8,9,10,11,12, 13,14,15] with anomalous dimensions for a wider class of operators [16,17,18, 19 ,20,21,22].”
- A relation between approaches to integrability in superconformal Yang-Mills theory (2003, methodology): “Initially in some special cases [9] and later in greater generality [10,11] following additional work [12,13], it has been argued that the one-loop anomalous dimension operator can be interpreted as one of the commuting Hamiltonians of an integrable spin chain.”