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Five loop Konishi from AdS/CFT

Zoltan Bajnok, Arpad Hegedus, Romuald A. Janik, Tomasz Lukowski

TL;DR

This work computes the perturbative five-loop anomalous dimension of the Konishi operator in N=4 SYM using finite-size (wrapping) corrections from the integrable AdS5xS5 worldsheet theory. It extends the Luscher formalism to multimagnon states, incorporating an intricate dressing phase via BES/BHL coefficients and revealing a nontrivial modification of ABA quantization at this order. The final result, Δ_w^(10) = -11340 + 2592 ζ(3) - 5184 ζ(3)^2 - 11520 ζ(5) + 30240 ζ(7), exhibits a pure transcendental structure and cancellation of mu-terms, serving as a stringent consistency check for excited-state TBA systems. The paper also reports a five-loop wrapping correction for a L=2 single-impurity state in the beta-deformed theory, highlighting the broader applicability to AdS/CFT spectral problems.

Abstract

We derive the perturbative five loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L=2 single impurity state in the beta deformed theory, which may be within reach of a direct perturbative computation. The Konishi expression exhibits two new features - a modification of Asymptotic Bethe Ansatz quantization and sensitiveness to an infinite set of coefficients of the BES/BHL dressing phase. The result satisfies nontrivial self-consistency conditions - simple transcendentality structure and cancellation of mu-term poles. It may be a testing ground for the proposed AdS/CFT TBA systems.

Five loop Konishi from AdS/CFT

TL;DR

This work computes the perturbative five-loop anomalous dimension of the Konishi operator in N=4 SYM using finite-size (wrapping) corrections from the integrable AdS5xS5 worldsheet theory. It extends the Luscher formalism to multimagnon states, incorporating an intricate dressing phase via BES/BHL coefficients and revealing a nontrivial modification of ABA quantization at this order. The final result, Δ_w^(10) = -11340 + 2592 ζ(3) - 5184 ζ(3)^2 - 11520 ζ(5) + 30240 ζ(7), exhibits a pure transcendental structure and cancellation of mu-terms, serving as a stringent consistency check for excited-state TBA systems. The paper also reports a five-loop wrapping correction for a L=2 single-impurity state in the beta-deformed theory, highlighting the broader applicability to AdS/CFT spectral problems.

Abstract

We derive the perturbative five loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L=2 single impurity state in the beta deformed theory, which may be within reach of a direct perturbative computation. The Konishi expression exhibits two new features - a modification of Asymptotic Bethe Ansatz quantization and sensitiveness to an infinite set of coefficients of the BES/BHL dressing phase. The result satisfies nontrivial self-consistency conditions - simple transcendentality structure and cancellation of mu-term poles. It may be a testing ground for the proposed AdS/CFT TBA systems.

Paper Structure

This paper contains 19 sections, 139 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Main features of the 5-loop Konishi computation
  3. Multiparticle Lüscher formulas and ABA modification
  4. TBA for diagonal scattering
  5. TBA for excited states by analytical continuation
  6. Multiparticle Lüscher formulas
  7. The dressing phase in the Lüscher kinematics
  8. BES dressing phase for physical particles
  9. BES dressing phase in the Lüscher kinematics
  10. BES dressing phase in the Lüscher kinematics from the DHM integral formula
  11. The Konishi computation
  12. Asymptotic Bethe Ansatz for the Konishi operator
  13. The general structure of the wrapping correction
  14. The 5-loop integrand
  15. Integration
  16. ...and 4 more sections

Figures (1)

  • Figure 1: F-term of the Lüscher correction corresponds to virtual particles propagating around the worldsheet and scattering with the Konishi two-particle state, $a$ and $b$ denote internal states of the virtual particle while $q$ is its 'mirror' momentum.