Towards the construction of N = 2 supersymmetric integrable hierarchies |
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Affiliation: | 1. International School for Advanced Studies (SISSA/ISAS), Via Beirut 2, 34014 Trieste, Italy;2. Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Moscow Region, Russia;1. School of Mathematics and Statistics, Henan University, Kaifeng, 475004, China;2. Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA |
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Abstract: | We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible N = 2 supersymmetric integrable hierarchies with N = 2 super-Wn second Hamiltonian structure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions. To this end we construct the N = 2 supersymmetric extensions of the Generalized Non-Linear Schrödinger hierarchy by exhibiting the corresponding super Lax operator. To find the correct Hamiltonians we are led to a new definition of super-residues for degenerate N = 2 supersymmetric pseudo-differential operators. We have found a new non-polynomials Miura-like realization for N = 2 superconformal algebra in terms of two bosonic chiral-anti-chiral free superfields. |
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