Wrapping in maximally supersymmetric and marginally deformed N=4 Yang-Mills

TL;DR

This paper investigates the spectral equivalence of certain spin chains in deformed N=4 Yang-Mills theory, providing explicit calculations of wrapping corrections and revealing symmetry properties across different deformations.

Contribution

It demonstrates the equality of spectra, including wrapping effects, for real deformations in the SU(2)-sector spin chain of marginally beta-deformed N=4 Yang-Mills, extending understanding of spectral properties.

Findings

First wrapping correction computed for undeformed magnon at momentum pi.

First wrapping correction derived for the beta=1/2 magnon for all even L.

Maximal transcendentality terms match for both magnons across all L.

Abstract

In this note we give evidence for an equality of the spectra, including wrapping, of the SU(2)-sector spin chain for real deformations beta and beta+1/L, in marginally beta-deformed N=4 Yang-Mills, which appears after relaxing the cyclicity constraint. Evidence for the equality is given by evaluating the first wrapping correction to the energy of the undeformed magnon of momentum pi, and the beta=1/2, physical magnon, for several spin chain lengths L. We also show that the term of maximal transcendentality coincides for both magnons to all L. As a by-product we provide an expression for the first wrapping correction to the beta = 1/2 single-magnon operator dimension, valid for all even L. We then apply the symmetry to the magnon dispersion relation of N=4, obtaining its first wrapping correction for a discrete set of magnon momenta.