Lectures on Yangian symmetry Article Swipe
YOU?
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· 2016
· Open Access
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· DOI: https://doi.org/10.1088/1751-8113/49/32/323002
· OA: W2413474658
In these introductory lectures we discuss the topic of Yangian symmetry from\nvarious perspectives. Forming the classical counterpart of the Yangian and an\nextension of ordinary Noether symmetries, first the concept of nonlocal charges\nin classical, two-dimensional field theory is reviewed. We then define the\nYangian algebra following Drinfeld's original motivation to construct solutions\nto the quantum Yang-Baxter equation. Different realizations of the Yangian and\nits mathematical role as a Hopf algebra and quantum group are discussed. We\ndemonstrate how the Yangian algebra is implemented in quantum, two-dimensional\nfield theories and how its generators are renormalized. Implications of Yangian\nsymmetry on the two-dimensional scattering matrix are investigated. We\nfurthermore consider the important case of discrete Yangian symmetry realized\non integrable spin chains. Finally we give a brief introduction to Yangian\nsymmetry in planar, four-dimensional super Yang-Mills theory and indicate its\nimpact on the dilatation operator and tree-level scattering amplitudes. These\nlectures are illustrated by several examples, in particular the two-dimensional\nchiral Gross-Neveu model, the Heisenberg spin chain and N=4 superconformal\nYang-Mills theory in four dimensions. This review arose from lectures given at\nthe Young Researchers Integrability School at Durham University (UK).\n
