The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability

By N. Beisert. 2004

828 citations recorded by the source corpus.

Abstract In this work we review recent progress in four-dimensional conformal quantum field theories and scaling dimensions of local operators. Here we consider the example of maximally supersymmetric gauge theory and present techniques to derive, investigate and apply the dilatation operator which measures the scaling dimensions. We construct the dilatation operator by purely algebraic means: Relying on the symmetry algebra and structural properties of Feynman diagrams we are able to bypass involved, higher-loop field theory computations. In this way we obtain the complete one-loop dilatation operator and the planar, three-loop deformation in an interesting subsector. These results allow us to address the issue of integrability within a planar four-dimensional gauge theory: We prove that the complete dilatation generator is integrable at one loop and present the corresponding Bethe ansatz. We furthermore argue that integrability extends to three loops and beyond. Assuming that it holds indeed, we finally construct a novel spin chain model at five loops and propose a Bethe ansatz which might be valid at arbitrary loop order!

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/dd50c091f9265d61a0c0b4af71186583be0f74a1

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In Geometry and Topology

1. S. Frolov
2. A. Tseytlin
3. N. Beisert
4. G. Arutyunov
5. R. Roiban
6. Romuald A. Janik
7. M. Staudacher
8. K. Zarembo

In Mathematical Physics

1. S. Frolov
2. A. Tseytlin
3. K. Zarembo
4. R. Roiban
5. Romuald A. Janik
6. D. Gaiotto
7. N. Beisert
8. N. Drukker

In Nuclear and High Energy Physics

1. S. Frolov
2. A. Tseytlin
3. N. Beisert
4. G. Arutyunov
5. M. Staudacher
6. R. Roiban
7. K. Zarembo
8. Romuald A. Janik

Citations in the corpus

• The su(2|2) dynamic S-matrix (2005, background): “the reviews [5–7].”
• The dilatation operator of conformal N=4 super-Yang–Mills theory (2003, background): “Beisert, Kristjansen and Staudacher [36] developed a more efficient means of calculating the matrix of anamolous dimensions for the vacuum N = 4 SYM case which is dual to a string theory on AdS5 × S(5) by introducing a dilatation operator D:”
• Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings (2005, neutral): “(2.2) In this paper we consider a small coupling constant g and apply perturbation theory.”
• Five loop Konishi from AdS/CFT (2009, background): “the light-cone quantized Green-Schwartz superstring is currently almost completed. Historically, the developments which led to it concentrated on the Bethe Ansatz part mostly on the gauge theory side [11, 12, 13, 14, 15] as well as for classical string solutions in AdS5 × S5 [16, 17]. Later this was”
• A relation between approaches to integrability in superconformal Yang-Mills theory (2003, background): “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.”
• Conformal Regge theory (2012, methodology): “In the following we review some definitions needed for the computation, following closely [64] and then apply it to our case.”
• Yang-Mills duals for semiclassical strings on AdS5 × S5 (2003, background): “ains information about all orders in λ, but the integrability of the dilatation operator has been established only at one-loop, although there are hints that integrability can be taken further in SYM [35,36], as well as cautions [37]. Nevertheless, it has been recently pointed out that the AdS5×S5 s”
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills (2004, methodology): “The calculation ofanom alous dim ensions oflocalcom posite operators in a conform al quantum eld theory such asN = 4 gaugetheory in fourdim ensionsisdi culteven in perturbation theory.”
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, background): “It is known that in N = 4 SYM there are sectors of operators closed under the action of the dilatation operator; see [9] and references therein.”
• On three-point correlation functions in the gauge/gravity duality (2010, background): “The corresponding spin chain Hamiltonian includes next to neighbour interactions [47],”
• Pulsating strings on Ads(5) x S(5) (2004, background): “tended to the full 1-loop SU(2,2|4) chain [35, 36], taking advantage of previous results on integrability in QCD amplitudes [37, 38]. Progress on higher orders in closed subsectors has also been made [39, 40, 41, 42]. The integrable spin chain formulation exposes the conserved charges. Conserved cha”
• The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, background): “Even more interestingly, the techniques of integrability allow in principle for an exact quantization of the superstring in AdS5 × S5 and/or the determination of anomalous dimensions in the N = 4 SYM.”
• Tailoring three-point functions and integrability (2010, background): “These states are denoted by (n,L) and they diagonalize the two-loop Hamiltonian of [59].”