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We demonstrate the equivalence between the worldsheet one-loop partitionfunctions computed near classical string solutions in the Green-Schwarz and inthe pure-spinor formulations of superstrings in AdS(5) x S(5). While theirbosonic sectors are the same in the conformal gauge, their fermionic sectorssuperficially appear to be very different (first vs second derivative kineticterms, presence vs absence of fermionic gauge symmetry). Still, we show thatthe quadratic fluctuation spectrum of sixteen fermionic modes of thepure-spinor formulation is the same as in the Green-Schwarz superstring and thecontribution of the extra "massless" fermionic modes cancels against that ofthe pure-spinor ghosts. We also provide evidence for a similar semiclassicalequivalence between the Green-Schwarz and the hybrid formulations ofsuperstrings in AdS(2) x S(2) x T(6) by studying several particular examples ofstring solutions.

Semiclassical equivalence of Green-Schwarz and Pure-Spinor/Hybrid formulations of superstrings in AdS(5) x S(5) and AdS(2) x S(2) x T(6)