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Four loop twist two, BFKL, wrapping and strings

Zoltan Bajnok, Romuald A. Janik, Tomasz Lukowski

TL;DR

This work computes the leading four-loop wrapping correction to twist-two operator anomalous dimensions in N=4 SYM using multiparticle Lüscher corrections from the AdS5×S5 worldsheet theory. The authors derive a compact expression for the wrapping energy, determine the complete γ_8^{wrapping}(M) in terms of harmonic sums and zeta values, and show that the correction preserves the cusp (large M) behavior while curing the analytic structure under M → −1 + ω to agree with LO and NLO BFKL predictions. The results reinforce the consistency between string-theory methods and perturbative gauge theory constraints, and they offer a path toward understanding higher-twist wrapping effects and reciprocity properties.

Abstract

The anomalous dimensions of twist two operators have to satisfy certain consistency requirements derived from BFKL. For N=4 SYM it was shown that at four loops, the anomalous dimensions derived from the all-loop asymptotic Bethe ansatz do not pass this test. In this paper we obtain the remaining wrapping part of these anomalous dimensions from string theory and show that these contributions exactly cure the problem and lead to agreement with both LO and NLO BFKL expectations.

Four loop twist two, BFKL, wrapping and strings

TL;DR

This work computes the leading four-loop wrapping correction to twist-two operator anomalous dimensions in N=4 SYM using multiparticle Lüscher corrections from the AdS5×S5 worldsheet theory. The authors derive a compact expression for the wrapping energy, determine the complete γ_8^{wrapping}(M) in terms of harmonic sums and zeta values, and show that the correction preserves the cusp (large M) behavior while curing the analytic structure under M → −1 + ω to agree with LO and NLO BFKL predictions. The results reinforce the consistency between string-theory methods and perturbative gauge theory constraints, and they offer a path toward understanding higher-twist wrapping effects and reciprocity properties.

Abstract

The anomalous dimensions of twist two operators have to satisfy certain consistency requirements derived from BFKL. For N=4 SYM it was shown that at four loops, the anomalous dimensions derived from the all-loop asymptotic Bethe ansatz do not pass this test. In this paper we obtain the remaining wrapping part of these anomalous dimensions from string theory and show that these contributions exactly cure the problem and lead to agreement with both LO and NLO BFKL expectations.

Paper Structure

This paper contains 13 sections, 101 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Twist two operators and BFKL
  3. Wrapping correction for twist two operators
  4. Main ingredients of the wrapping correction
  5. The calculation of the wrapping correction
  6. Determination of the final form of $\gamma_8^{wrapping}(M)$
  7. Large $M$ asymptotics of $\gamma_8^{wrapping}(M)$
  8. Analytical continuation of $\gamma_8^{wrapping}(M)$
  9. Conclusions
  10. Evaluation of the integrand
  11. Exact calculation of the coefficient of $\zeta(3)$ and $\zeta(5)$
  12. Analytical continuation of harmonic sums
  13. Explicit S-matrix coefficients

Figures (1)

  • Figure 1: Multiparticle Lüscher correction. The vertical lines represent the physical particles forming the multiparticle state, while the double line loop represents the on-shell 'virtual' particle with complex momentum.