Semiclassical equivalence of Green-Schwarz and pure-spinor/hybrid formulations of superstrings in AdS5 x S5 and AdS2 x S2 x T6

We demonstrate the equivalence between the worldsheet one-loop partition functions computed near classical string solutions in the Green-Schwarz and in the pure-spinor formulations of superstrings in AdS(5) x S-5. While their bosonic sectors are the same in the conformal gauge, their fermionic sectors superficially appear to be very different (first versus second-derivative kinetic terms, presence versus absence of fermionic gauge symmetry). Still, we show that the quadratic fluctuation spectrum of 16 fermionic modes of the pure-spinor formulation is the same as in the Green-Schwarz superstring and the contribution of the extra 'massless' fermionic modes cancels against that of the pure-spinor ghosts. We also provide evidence for a similar semiclassical equivalence between the Green-Schwarz and the hybrid formulations of superstrings in AdS(2) x S-2 x T-6 by studying several particular examples of string solutions.