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

Abstract

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 AdS5 × S5. 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 AdS2 × S2 × T6 by studying several particular examples of string solutions.