One-loop corrections to AdS5 × S5 superstring partition function via Pohlmeyer reduction

Abstract

We discuss semiclassical expansions around a class of classical string configurations lying in AdS3 × S1 using the Pohlmeyer-reduced form of the AdS5 × S5 superstring theory. The Pohlmeyer reduction of the AdS5 × S5 superstring theory is a gauged Wess–Zumino–Witten model with an integrable potential and two-dimensional fermionic fields. It was recently conjectured that the quantum string partition function is equal to the quantum reduced theory partition function. Continuing the previous paper (Hoare et al 2009 J. Phys. A: Math. Theor. 42 375204), where arbitrary solutions in AdS2 × S2 and homogeneous solutions were considered, we provide an explicit demonstration of this conjecture at the one-loop level for several string solutions in AdS3 × S1 embedded into AdS5 × S5. Quadratic fluctuations derived in the reduced theory for inhomogeneous strings are equivalent to respective fluctuations found from the Nambu action in the original string theory. We also show the equivalence of fluctuation frequencies for homogeneous strings with both the orbital momentum and the winding on a big circle of S5.