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Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems

  • Chapter

Part of the CRM Series in Mathematical Physics book series (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.

Keywords

  • Gauge Theory
  • Gauge Group
  • Spectral Curve
  • Supersymmetric Gauge Theory
  • Gauge Algebra

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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