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Pure-spinor superstrings in d=2,4,6
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We continue the study of the d=2,4,6 pure-spinor superstring models introduced in [1]. By explicitly solving the pure-spinor constraint we show that these theories have vanishing central charge and work out the (covariant) current algebra for the Lorentz currents. We argue that these super-Poincare covariant models may be thought of as compactifications of the superstring on CY_{4,3,2}, and take some steps toward making this precise by constructing a map to the RNS superstring variables. We also discuss the relation to the so called hybrid superstrings, which describe the same type of compactifications.
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Vertex operators for the superstring with manifest $d=6$ $\mathcal{N}=1$ supersymmetry
A manifestly d=6 N=1 supersymmetric vertex operator and amplitude prescription are constructed for the superstring, with BRST invariance implying the SYM equations of motion.
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