On semiclassical analysis of pure spinor superstring in an AdS₅ × S⁵ background

Relation between semiclassical analyses of Green-Schwarz and pure spinor formalisms in an AdS₅ × S⁵ background is clarified. It is shown that the two formalisms have identical semiclassical partition functions for a simple family of classical solutions. It is also shown that, when the classical string is furthermore rigid, this in turn implies that the two formalisms predict the same one-loop corrections to spacetime energies.