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.
Delduc, F., & Sorin, A. S. (2002). Lax pair formulation of the N = 4 Toda chain (KdV) hierarchy in N = 4 superspace. Nuclear Physics B, 631(3), 403–425. https://doi.org/10.1016/S0550-3213(02)00275-4