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

TL;DR

This paper computes the four-loop anomalous dimension of the Konishi operator in N=4 SYM using integrable string theory methods, matching gauge theory results and extending Luscher formulas to multiparticle states.

Contribution

It introduces a novel multiparticle generalization of Luscher formulas for finite size effects in integrable models, applied to the Konishi operator at four loops.

Findings

Derived the four-loop anomalous dimension of Konishi from string theory.

Extended Luscher formulas to multiparticle states in integrable models.

Results agree with perturbative gauge theory computations.

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.