INTEGRABILITY IN QCD AND BEYOND

By A. Belitsky, V. Braun, A. Gorsky, G. Korchemsky. 2004

156 citations recorded by the source corpus.

Yang–Mills theories in four space–time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns out that the effective Yang–Mills dynamics in several important limits is described by completely integrable systems that prove to be related to the celebrated Heisenberg spin chain and its generalizations. In this review we explain the general phenomenon of complete integrability and its realization in several different situations. As a prime example, we consider in some detail the scale dependence of composite (Wilson) operators in QCD and super-Yang–Mills (SYM) theories. High-energy (Regge) behavior of scattering amplitudes in QCD is also discussed and provides one with another realization of the same phenomenon that differs, however, from the first example in essential details. As the third example, we address the low-energy effective action in a SYM theory which, contrary to the previous two cases, corresponds to a classical integrable model. Finally, we include a short overview of recent attempts to use gauge/string duality in order to relate integrability of Yang–Mills dynamics with the hidden symmetry of a string theory on a curved background.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e4c5c1e35711959f557d677a65047ffb8d459b10

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In Nuclear and High Energy Physics

1. S. Frolov
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Citations in the corpus

• Foundations of the AdS5 × S5 superstring: I (2009, background): “To get more familiar with gauge theory constructions, the reader is invited to consult the original literature and reviews [10, 11].”
• Entanglement in many-body systems (2007, background): “They account for the effective interactions in a variety of very different physical contexts ranging from high energy to nuclear physics (Belitsky et al., 2004; Polyakov, 1977).”
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, background): “[52–55]).”
• The factorized S-matrix of CFT/AdS (2004, background): “Integrable structures have appeared before in planar QCD, starting with the pioneering work of Lipatov [4] (for a comprehensive review, see [5]).”
• Algebraic Curve for the SO(6) Sector of AdS/CFT (2004, background): “cal operators. It was subsequently shown that integrability not only extends to all local single-trace operators of N = 4 SYM [28,29] (extending earlier findings of integrability in gauge theory, c.f. [30] for a review), but more surprisingly also to higher loops (at least in some subsectors) [31,32]”
• The analytic Bethe ansatz for a chain with centrally extended symmetry (2006, background): “of non-interacting IIB superstring theory on AdS 5 × S5 [7,8] provides hope that their spectrum can be computed exactly at finite coupling gby means of Bethe equations [9], cf. the reviews [10,11] and [12]. The underlying integrable model of AdS/CFT is best described as a two-dimensional sigma model ”
• Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings (2005, background): “References to further interesting work on integrability in QCD may be found in [6].”
• Complete spectrum of long operators in N=4 SYM at one loop (2005, background): “Subsequently, integrability of evolution equations for quasipartonic operators was found also in QCD and less supersymmetric theories [9] (see [10] for a recent review).”
• Semiclassical Strings and AdS/CFT (2004, background): “2Relations between 1-loop anomalous dimension matrix for a certain class of composite operators and integrable spin chain Hamiltonians were observed previously in the large N QCD context [63] (for a review and connections to AdS/CFT see [64]).”
• Spiky strings and single trace operators in gauge theories (2004, background): “An interesting summary on the relation between previous work in QCD and the more recent work can be found in [33].”
• Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory (2005, background): “For dilatation operators and associated integrable spin chains in less supersymmetric gauge theories see also [ 26 ] and references therein.”
• Classical/quantum integrability in non-compact sector of AdS/CFT (2004, background): “The mixing matrix acts pairwise on the nearest-neighbor sites of the lattice and turns out to coincide with the Hamiltonian of the integrable spin s = −1/2 XXX spin chain [42, 4] which is similar to the spin s = −1 [53, 54, 55, 56] and s = −3/2 [57, 55, 56] chains that describe anomalous dimensions ”