Light-cone Gauge NSR Strings in Noncritical Dimensions

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Light-cone gauge NSR string theory in noncritical dimensions should correspond to a string theory with a nonstandard longitudinal part. Supersymmetrizing the bosonic case [arXiv:0909.4675], we formulate a superconformal worldsheet theory for the longitudinal variables X±, ψ±. We show that with the transverse variables and the ghosts combined, it is possible to construct a nilpotent BRST charge.