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Two-Dimensional Supergravities, Hidden Symmetries and Integrable Systems

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Particle Physics

Part of the book series: NATO ASI Series ((NSSB,volume 173))

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Abstract

Present interest in two-dimensional field-theories is dominated by the all-important role they play in string and superstring theories. This is understandable in view of the eminence of superstrings as prime candidates for the ultimate unification of fundamental interactions1, but it makes us forget that the special role of two dimensions was already recognized long before the advent of superstrings. While the two-dimensional theories relevant to strings are all conformally invariant2, 3 (and really nothing but free field theories), there exist many examples of two-dimensional systems without conformai invariance which are not free theories but nonetheless exactly solvable both at the classical and the quantum level4. These properties are related to two peculiarities of two-dimensional physics. One is the emergence of infinite-dimensional symmetries. For instance, the conformai group is infinite-dimensional in d=2 but not for d>2. Symmetries of the Kac-Moody type5 play an important role not only in (compactified) string theories but also in d=2 general relativity6, 7, 8 and nonlinear σ-models9. The other peculiarity is the indistinguishability of bosons and fermions which was first noticed in the guise of the equivalence of the Thirring model with the sine-Gordon theory10; again, this feature is not restricted to the conformally invariant theories.

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Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Karlsruhe, Germany

    Hermann Nicolai

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  1. Hermann Nicolai
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Editors and Affiliations

  1. Laboratory of Theoretical Physics and High Energies, Université Pierre et Marie Curie, Paris, France

    Maurice Lévy  & Jean-Louis Basdevant  & 

  2. Theory Division, C.E.R.N., Geneva, Switzerland

    Maurice Jacob

  3. Institute of Theoretical Physics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    David Speiser  & Jacques Weyers  & 

  4. Institute of Theoretical Physics, Katholieke Universiteit Leuven, Leuven, Belgium

    Raymond Gastmans

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© 1988 Plenum Press, New York

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Nicolai, H. (1988). Two-Dimensional Supergravities, Hidden Symmetries and Integrable Systems. In: Lévy, M., Basdevant, JL., Jacob, M., Speiser, D., Weyers, J., Gastmans, R. (eds) Particle Physics. NATO ASI Series, vol 173. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0977-2_3

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  • DOI: https://doi.org/10.1007/978-1-4613-0977-2_3

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