Gluing Hexagons at Three Loops

Abstract

We perform extensive three-loop tests of the hexagon bootstrap approach for structure constants in planar $\mathcal{N}=4$ SYM theory. We focus on correlators involving two BPS operators and one non-BPS operator in the so-called $SL(2)$ sector. At three loops, such correlators receive wrapping corrections from mirror excitations flowing in either the adjacent or the opposing channel. Amusingly, we find that the first type of correction coincides exactly with the leading wrapping correction for the spectrum (divided by the one-loop anomalous dimension). We develop an efficient method for computing the second type of correction for operators with any spin. The results are in perfect agreement with the recently obtained three-loop perturbative data by Chicherin, Drummond, Heslop, Sokatchev [2] and by Eden [3]. We also derive the integrand for general multi-particle wrapping corrections, which turns out to take a remarkably simple form. As an application we estimate the loop order at which various new physical effects are expected to kick-in.

24 pages, 7 figures

References in corpus (7)

• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• Three-loop universal structure constants in N=4 susy Yang-Mills theory
• The four-loop six-gluon NMHV ratio function

Cited by in corpus (2)

• A study of integrable form factors in massless relativistic AdS_3
• Half-BPS half-BPS twist two at four loops in N=4 SYM