`Analytic Continuation' of N=2 Minimal Model

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In this paper we discuss what theory should be identified as the `analytic continuation' with N → -N of the N=2 minimal model with the central charge c = 1 - 2/N. We clarify how the elliptic genus of the expected model is written in terms of holomorphic linear combinations of the `modular completions' introduced in [arXiv:1012.5721 [hep-th]] in the SL(2)ₙ₊₂/U(1)-supercoset theory. We further discuss how this model could be interpreted as a kind of `compactified' model of the SL(2)ₙ₊₂/U(1)-supercoset in the (R,R)-sector, in which only the discrete spectrum appears in the torus partition function and the potential IR-divergence due to the non-compactness of target space is removed. We also briefly argue on possible definitions of the sectors with other spin structures.