TY - JOUR

T1 - Baxter equation beyond wrapping

AU - Belitsky, Andrei

N1 - Funding Information:
This work was supported by the US National Science Foundation under grant no. PHY-0456520. We would like to thank Stefan Zieme for renewing the author's interest in questions discussed here, Romuald Janik for useful correspondence and Yuri Dokshitzer, Gavin Salam and Gregory Korchemsky for hospitality at Jussieu and Saclay, respectively, in December of 2008 when this work was initiated.

PY - 2009/6/15

Y1 - 2009/6/15

N2 - The Baxter-like functional equation encoding the spectrum of anomalous dimensions of Wilson operators in maximally supersymmetric Yang-Mills theory available to date ceases to work just before the onset of wrapping corrections. In this Letter, we work out an improved finite-difference equation by incorporating nonpolynomial effects in the transfer matrix entering as its ingredient. This yields a self-consistent asymptotic finite-difference equation valid at any order of perturbation theory. Its exact solutions for fixed spins and twists at and beyond wrapping order give results coinciding with the ones obtained from the asymptotic Bethe Ansatz. Correcting the asymptotic energy eigenvalues by the Lüscher term, we compute anomalous dimensions for a number of short operators beyond wrapping order.

AB - The Baxter-like functional equation encoding the spectrum of anomalous dimensions of Wilson operators in maximally supersymmetric Yang-Mills theory available to date ceases to work just before the onset of wrapping corrections. In this Letter, we work out an improved finite-difference equation by incorporating nonpolynomial effects in the transfer matrix entering as its ingredient. This yields a self-consistent asymptotic finite-difference equation valid at any order of perturbation theory. Its exact solutions for fixed spins and twists at and beyond wrapping order give results coinciding with the ones obtained from the asymptotic Bethe Ansatz. Correcting the asymptotic energy eigenvalues by the Lüscher term, we compute anomalous dimensions for a number of short operators beyond wrapping order.

UR - http://www.scopus.com/inward/record.url?scp=66149132291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=66149132291&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2009.05.004

DO - 10.1016/j.physletb.2009.05.004

M3 - Article

AN - SCOPUS:66149132291

SN - 0370-2693

VL - 677

SP - 93

EP - 99

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 1-2

ER -