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Advances in High Energy Physics
Volume 2015 (2015), Article ID 762481, 21 pages
Research Article

Reciprocity and Self-Tuning Relations without Wrapping

1Sezione INFN di Bologna, Dipartimento di Fisica e Astronomia, Università di Bologna, Via Irnerio 46, 40126 Bologna, Italy
2Dipartimento di Fisica dell’Università della Calabria, Arcavacata, Rende, 87036 Cosenza, Italy
3Laboratoire Jean Alexandre Dieudonné, Université Nice Sophia Antipolis, 06100 Nice, France
4Dipartimento di Fisica dell’Università della Calabria and INFN, Gruppo Collegato di Cosenza, Arcavacata, Rende, 87036 Cosenza, Italy

Received 6 August 2015; Accepted 15 October 2015

Academic Editor: Stefano Moretti

Copyright © 2015 Davide Fioravanti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We consider scalar Wilson operators of = 4 SYM at high spin, , and generic twist in the multicolor limit. We show that the corresponding (non)linear integral equations (originating from the asymptotic Bethe Ansatz equations) respect certain “reciprocity” and functional “self-tuning” relations up to all terms (inclusive) at any fixed ’t Hooft coupling . Of course, this relation entails straightforwardly the well-known (homonymous) relations for the anomalous dimension at the same order in . On this basis we give some evidence that wrapping corrections should enter the nonlinear integral equation and anomalous dimension expansions at the next order , at fixed ’t Hooft coupling, in such a way to reestablish the aforementioned relation (which fails otherwise).