Finite-Size Corrections to Anomalous Dimensions in N=4 SYM Theory

TL;DR

The paper addresses finite-size (1/L) corrections to anomalous dimensions of large N=4 SYM operators by analyzing the SU(2) Heisenberg spin-chain obtained from one-loop dilatation and solving the Bethe equations in a large-L scaling regime. It shows that the Bethe roots are governed by an associated Laguerre polynomial structure, enabling a residue-based computation that yields γ = (λ n^2 α(1-α))/(2L) (1+1/L) + O(1/L^3) (equivalently γ = λ m(n-m)/(2L) (1+1/L) + O(1/L^3)). This provides a concrete gauge-theory prediction for finite-size corrections that should match quantum corrections on the AdS5×S5 string side and opens the door to generalizing the analysis to arbitrary Bethe states using loop equations, resolvents, and Baxter Q-operator techniques.

Abstract

The scaling dimensions of large operators in N=4 supersymmetric Yang-Mills theory are dual to energies of semiclassical strings in AdS(5)xS(5). At one loop, the dimensions of large operators can be computed with the help of Bethe ansatz and can be directly compared to the string energies. We study finite-size corrections for Bethe states which should describe quantum corrections to energies of extended semiclassical strings.