Lax pair formulation of the N = 4 Toda chain (KdV) hierarchy in N = 4 superspace

  • Delduc F
  • Sorin A
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Abstract

Lax pair and Hamiltonian formulations of the N = 4 supersymmetric Toda chain (KdV) hierarchy in N = 4 superspace are proposed. The general formulae for the infinite tower of its bosonic flows in terms of the Lax operator in N = 4 superspace are derived. A new N = 4 superfield basis in which the flows are local is constructed and its embedding in the N = 4 O(4) superconformal supercurrent is established. A proof that the flows possess five complex conjugations and an infinite-dimensional group of discrete symmetries in N = 4 superspace is presented. A relation between the two descriptions of the hierarchy in N = 4 superspace used in the literature is established. All known N = 2 superfield representations of the N = 4 KdV hierarchy are shown to derive from our N = 4 superspace Lax representation. © 2002 Published by Elsevier Science B.V.

Author-supplied keywords

  • Completely integrable systems
  • Discrete symmetries
  • Supersymmetry
  • Toda field theory

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Authors

  • F. Delduc

  • A. S. Sorin

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