# A relation between approaches to integrability in superconformal Yang-Mills theory

@article{Dolan2003ARB, title={A relation between approaches to integrability in superconformal Yang-Mills theory}, author={Louise A Dolan and Chiara R. Nappi and Edward Witten}, journal={Journal of High Energy Physics}, year={2003}, volume={2003}, pages={017-017} }

We make contact between the infinite-dimensional non-local symmetry of the type-IIB superstring on AdS5 × S5 and a non-abelian infinite-dimensional symmetry algebra for the weakly coupled superconformal gauge theory. We explain why the planar limit of the one-loop dilatation operator is the hamiltonian of a spin chain, and show that it commutes with the g2N = 0 limit of the non-abelian charges.

## 257 Citations

Spin Models and Superconformal Yang-Mills Theory

- Physics, Mathematics
- 2005

Abstract We apply novel techniques in planar superconformal Yang–Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with…

Yangian Symmetry and Integrability of Planar N=4 Supersymmetric Yang-Mills Theory.

- Physics, MathematicsPhysical review letters
- 2017

It is proved that the classical equations of motion of the model close onto themselves under the action of Yangian generators, and the relationship serves as a criterion for integrability in planar gauge theories by explicitly checking that it applies to the integrable Aharony-Bergman-Jafferis-Maldacena theory but not to the nonintegrable N=1 supersymmetric Yang-Mills theory.

Aspects of Integrability in N =4 SYM

- Physics
- 2007

Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding…

Classical/quantum integrability in non-compact sector of AdS/CFT

- Physics
- 2004

We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of…

N=2 Super Yang–Mills and the XXZ spin chain

- Physics
- 2005

Abstract We analyse the renormalisation properties of composite operators of scalar fields in the N = 2 Super Yang–Mills theory. We compute the matrix of anomalous dimensions in the planar limit at…

T-Duality, dual conformal symmetry and integrability for strings on AdS5 × S5

- Physics
- 2009

In recent years two intriguing observations have been made for = 4 super Yang–Mills theory and for superstrings on AdS5 × S5: In the planar limit the computation of the spectrum is vastly simplified…

Yangian Symmetry in D=4 Superconformal Yang-Mills Theory

- Physics
- 2004

We will discuss an integrable structure for weakly coupled superconformal Yang-Mills theories, describe certain equivalences for the Yangian algebra, and fill a technical gap in our previous study of…

Integrable Open Spin Chains in Defect Conformal Field Theory

- Physics
- 2004

We demonstrate that the one-loop dilatation generator for the scalar sector of a certain perturbation of N=4 Super Yang-Mills with fundamentals is the Hamiltonian of an integrable spin chain with…

The algebra of transition matrices for the AdS 5 × S 5 superstring

- Physics
- 2004

We consider integrability properties of the superstring on AdS5 × S5 background and construct a new one parameter family of currents which satisfies the vanishing curvature condition. We present the…

On hidden symmetries of a super gauge theory and twistor string theory

- Physics
- 2005

We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the -extented self-dual super Yang-Mills equations for general ≤ 4 by using…

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