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We construct freely acting asymmetric Z₄ orbifolds of type IIB string theory on T⁵ preserving 24, 16 or 8 supercharges in five dimensions. We show that these models are well-defined if the SO (8) lattice is chosen, while the SU (2) ⁴ lattice, which was previously considered in the literature, does not lead to a modular invariant partition function. Also, we clarify some issues related to the coefficients in the qq-expansion of the partition function in the twisted sectors of asymmetric orbifolds.
George Gkountoumis (Fri,) studied this question.
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