We address some issues relating to a supersymmetric (SUSY) Ward-Takahashi (WT) identity in Sugino's lattice formulation of two-dimensional (2D) N = (2, 2) SU (k) supersymmetric Yang-Mills theory (SYM). A perturbative argument shows that the SUSY WT identity in the continuum theory is reproduced in the continuum limit without any operator renormalization/mixing and tuning of lattice parameters. As application of the lattice SUSY WT identity, we show that a prescription for the Hamiltonian density in this lattice formulation, proposed by Kanamori, Sugino and Suzuki, is justified also from a perspective of an operator algebra among correctly-normalized supercurrents. We explicitly confirm the SUSY WT identity in the continuum limit to the first nontrivial order in a semi-perturbative expansion. © 2009 Elsevier B.V. All rights reserved.
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