One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction

TL;DR

This paper verifies the equivalence of one-loop quantum corrections to string partition functions in AdS_5 x S^5 using Pohlmeyer reduction, demonstrating the conjecture that reduced theory reproduces the original string theory results.

Contribution

It provides explicit one-loop calculations confirming the equivalence between the original superstring theory and its Pohlmeyer-reduced form for specific classical solutions.

Findings

Quadratic fluctuations in the reduced theory match those in the original string theory.

Fluctuation frequencies are equivalent for homogeneous strings with momentum and winding.

The conjecture holds at the one-loop level for various solutions in AdS_3 x S^1.

Abstract

We discuss semiclassical expansions around a class of classical string configurations lying in AdS_3 x S^1 using the Pohlmeyer-reduced from of the AdS_5 x S^5 superstring theory. The Pohlmeyer reduction of the AdS_5 x S^5 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 (arXiv:0906.3800) where arbitrary solutions in AdS_2 x S^2 and homogeneous solutions were considered, we provide explicit demonstration of this conjecture at the one-loop level for several string solutions in AdS_3 x S^1 embedded into AdS_5 x S^5. 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 S^5.