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Theoretical Physics at the End of the Twentieth Century pp 1–125Cite as

Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems

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Part of the book series: CRM Series in Mathematical Physics ((CRM))

Abstract

We present a series of four self-contained lectures on the following topics;

  1. (I)

    An introduction to 4-dimensional 1 ≤ N ≤ 4 supersymmetric Yang-Mills theory, including particle and field contents, N = 1 and N = 2 superfield methods and the construction of general invariant Lagrangians;

  2. (II)

    A review of holomorphicity and duality in N = 2 super-Yang-Mills, of Seiberg-Witten theory and its formulation in terms of Riemann surfaces;

  3. (III)

    An introduction to mechanical Hamiltonian integrable systems; such as the Toda and Calogero-Moser systems associated with general Lie algebras; a review of the recently constructed Lax pairs with spectral parameter for twisted and untwisted elliptic Calogero-Moser systems;

  4. (IV)

    A review of recent solutions of the Seiberg-Witten theory for general gauge algebra and adjoint hypermultiplet content in terms of the elliptic Calogero-Moser integrable systems.

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  1. Eric D’Hoker
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  2. D. H. Phong
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  1. Département de Mathématiques et Statistique, Université de Montréal, Succursale Centre-ville, C.P. 6128, H3C 3J7, Montréal, Québec, Canada

    Yvan Saint-Aubin

  2. Department of Physics and Department of Mathematics and Statistics, McGill University, James Administration Building, Room 504, H3A 2T5, Montréal, Québec, Canada

    Luc Vinet

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D’Hoker, E., Phong, D.H. (2002). Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems. In: Saint-Aubin, Y., Vinet, L. (eds) Theoretical Physics at the End of the Twentieth Century. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3671-7_1

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