Planar Integrability and Yangian Symmetry in N=4 Supersymmetric Yang–Mills

Abstract: The discovery and utilisation of integrability in the planar limit of certain gauge and string theory models has made available many exciting non-perturbative results and insights for the AdS/CFT correspondence. In this talk I will introduce the prototypical AdS/CFT duality between string theory on AdS₅×S⁵ and N=4 supersymmetric Yang–Mills theory, and highlight the usefulness of planar integrability through some achievements. I will then present a formal notion of integrability as a hidden Yangian symmetry of the action. Importantly, this symmetry is realised on field theory objects in a non-standard fashion for which a rigorous framework to deal with its implications is lacking. I will demonstrate that this symmetry indeed leads to non-trivial relations for quantum correlations functions of this model. In order to make them work out, I also show in what sense the symmetry is compatible with BRST gauge fixing.

mathematical physics

Audience: researchers in the discipline

( video )

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