Auxiliary field methods in D = 2 (or 3), N = 2 supersymmetric (SUSY) non-linear sigma models (NLσMs) are studied. For these models auxiliary fields as Lagrange multipliers belong to a vector or a chiral superfield, which gives a Kähler quotient of complexified gauge group or a holomorphic constraint on it, respectively. Using these, NLσMs on all Hermitian symmetric spaces were formulated previously. In this paper, we formulate new SUSY NLσMs on some rank-two Kähler coset spaces as SUSY gauge theories with two Fayet-Iliopoulos parameters.
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