Deformations of N = 4 SYM and integrable spin chain models

By D. Berenstein, Sergey A. Cherkis. 2004

175 citations recorded by the source corpus.

Beginning with the planar limit of N=4 SYM theory, we study planar diagrams for field theory deformations of N=4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one-loop dilatation operator in the scalar sector, places very strong constraints on the field theory, so that the only soluble models correspond essentially to orbifolds of N=4 SYM. For these, the associated spin chain model gets twisted boundary conditions that depend on the length of the chain, but which are still integrable. We also show that theories with integrable subsectors appear quite generically, and it is possible to engineer integrable subsectors to have some specific symmetry, however these do not generally lead to full integrability. We also try to construct a theory whose spin chain has quantum group symmetry SOq(6) as a deformation of the SO(6) R-symmetry structure of N=4 SYM. We show that it is not possible to obtain a spin chain with that symmetry from deformations of the scalar potential of N=4 SYM. We also show that the natural context for these questions can be better phrased in terms of multi-matrix quantum mechanics rather than in four-dimensional field theories.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/da0355034e8a2b896c25f5539599f87c1dfb1d74

How researchers see this paper

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In Geometry and Topology

1. S. Frolov
2. G. Arutyunov
3. A. Tseytlin
4. N. Beisert
5. R. Roiban
6. P. Koroteev
7. L. Alday
8. K. Zoubos

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

1. S. Frolov
2. G. Arutyunov
3. A. Tseytlin
4. R. Roiban
5. K. Zoubos
6. L. Alday
7. N. Beisert
8. P. Koroteev

Citations in the corpus

• Beauty and the twist: the Bethe ansatz for twisted = 4 SYM (2005, unknown): “ar X iv :h ep -t”
• Green-Schwarz Strings in TsT-transformed backgrounds (2005, methodology): “In particular, it was successfully used in [1] to obtain a deformation of the AdS5×S(5) geometry which was conjectured to be dual to a supersymmetric marginal deformation of N = 4 SYM sometimes called a β deformation [4]-[6].”
• INTEGRABILITY IN QCD AND BEYOND (2004, background): “ dilatation operator was calculated in Refs. [80] up to three-loop order. Ultimately, one has to understand what symmetry of the quantum field theory is responsible for the appearance of integrability [81,82] and what part of it survives after decreasing the amount of supersymmetry [83–85], as we exp”
• Jordanian deformations of the AdS5 × S5 superstring (2014, unknown): “A promising way is to consider a twist of the q-deformation of the SO(6) sector argued in [48, 49].”
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries (2010, background): “As was first noted in [10], there exist integrable deformations of the algebraic structures at the N = 4 SYM point which do not have a good field theory interpretation, in the sense of arising as the one-loop hamiltonian of a deformed field theory.”
• Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, background): “In all previously discussed examples of similar comparisons the leading order terms in the two expressions matched, and our aim will be to extend this matching to the present (non-supersymmetric for unequal γi) case.”
• Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory (2005, background): “…the wellknown quantum dilaton shift properly taken into account [46]), or directly using the T-duality transformations spelled out in the context of the Green-Schwarz string in [47, 48], it is then not too hard to find the world sheet type IIB superstring action resulting from applying the…”
• Quantum deformations of the one-dimensional Hubbard model (2008, background): “nd Uq(su(3)) symmetry have indeed appeared in this context, in particular for so-called beta-deformed N = 4 gauge theory [45] with complex deformation parameter [46–48]. However, the argument used in [47] tells us that the symmetry considered in this paper cannot apply to conformal gauge theories su”