Matching quantum strings to quantum spins: One-loop vs. finite-size corrections

Abstract

We compare quantum corrections to semiclassical spinning strings in AdS 5 × S 5 to one-loop anomalous dimensions in N = 4 supersymmetric gauge theory. The latter are computed using the reduced (Landau–Lifshitz) sigma model and with the help of the Bethe ansatz. The results of all three approaches are in remarkable agreement with each other. As a byproduct we establish the relationship between linear instabilities in the Landau–Lifshitz model and analyticity properties of the Bethe ansatz.