Four-loop perturbative Konishi from strings and finite size effects for multiparticle states

TL;DR

This work develops generalized Luscher-type finite-size corrections for multiparticle states in integrable 2D theories and applies them to the AdS5×S5 worldsheet to extract the four-loop wrapping correction to the Konishi operator in N=4 SYM. By analyzing relativistic models (sinh-Gordon, Lee–Yang, sine-Gordon) they conjecture universal corrections to the Bethe–Yang quantization for multiparticle states and extend them to the non-relativistic AdS/CFT setting, including non-diagonal scattering and mirror theory. The authors sum over an infinite tower of antisymmetric SL(2) bound states in the mirror theory and compute the F-term contribution, obtaining $\Delta_{wrapping} E = (324+864\zeta(3)-1440\zeta(5))\,g^8$, in exact agreement with four-loop gauge theory results. This provides a stringent test of the integrable string description and clarifies the role of bound-state contributions in wrapping corrections.

Abstract

We derive the perturbative four loop anomalous dimension of the Konishi operator in N=4 SYM theory from the integrable string sigma model by evaluating the finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. We obtain these multiparticle generalizations of Luscher formulas by studying certain exactly solvable relativistic integrable quantum field theories. The final result involves a summation of all bound states in the mirror theory and agrees with gauge theory perturbative computations.

Figures (1)

• Figure 1: The result for the symmetric representation bound states.