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

TL;DR

The paper demonstrates a remarkable agreement between one-loop quantum string corrections and finite-size gauge-theory corrections in the AdS5×S5 / N=4 SYM correspondence. By connecting the Landau-Lifshitz sigma model to both the semiclassical string description and the Bethe-ansatz spin-chain approach, it shows that leading 1/J corrections in both pictures match, with the string theory providing a natural regularization for LL-mode sums. The analysis spans both SL(2) and SU(2) sectors, revealing an anomaly-driven finite-size correction and, in the SU(2) case, instabilities tied to pole crossings in the Bethe equations. The work outlines extensions to higher loops, the AFSS quantum-string Bethe framework, and SU(3) generalizations, highlighting open questions about a universal finite-size mechanism across classical string solutions.

Abstract

We compare quantum corrections to semiclassical spinning strings in AdS(5)xS(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.