Abstract
The link between BFKL physics and twist-two operators involves an analytical continuation in the spin of the operators away from the physical even integer values. Typically this is done only after obtaining an analytical result for integer spin through nested harmonic sums. In this paper we propose analyticity conditions for the solution of Baxter equation which would work directly for any value of complex spin and reproduce results from the analytical continuation of harmonic sums. We carry out explicit contructions up to 2-loop level. These nonstandard solutions of the Baxter equation have rather surprising asymptotics. We hope that these analyticity conditions may be used for incorporating them into the exact TBA/FiNLIE/QSC approaches valid at any coupling.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Lipatov, Reggeization of the vector meson and the vacuum singularity in non-Abelian gauge theories, Sov. J. Nucl. Phys. 23 (1976) 338 [Yad. Fiz. 23 (1976) 642] [INSPIRE].
E. Kuraev, L. Lipatov and V.S. Fadin, The Pomeranchuk singularity in non-Abelian gauge theories, Sov. Phys. JETP 45 (1977) 199 [Zh. Eksp. Teor. Fiz. 72 (1977) 377] [INSPIRE].
I. Balitsky and L. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [Yad. Fiz. 28 (1978) 1597] [INSPIRE].
A. Kotikov and L. Lipatov, DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory, Nucl. Phys. B 661 (2003) 19 [Erratum ibid. B 685 (2004) 405] [hep-ph/0208220] [INSPIRE].
R. Janik and R.B. Peschanski, High-energy scattering and the AdS/CFT correspondence, Nucl. Phys. B 565 (2000) 193 [hep-th/9907177] [INSPIRE].
R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115] [INSPIRE].
M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
A. Kotikov and L. Lipatov, Pomeron in the N = 4 supersymmetric gauge model at strong couplings, Nucl. Phys. B 874 (2013) 889 [arXiv:1301.0882] [INSPIRE].
R.A. Janik and P. Laskos-Grabowski, Approaching the BFKL Pomeron via integrable classical solutions, arXiv:1311.2302 [INSPIRE].
A. Kotikov, L. Lipatov, A. Rej, M. Staudacher and V. Velizhanin, Dressing and wrapping, J. Stat. Mech. 10 (2007) P10003 [arXiv:0704.3586] [INSPIRE].
Z. Bajnok, R.A. Janik and T. Lukowski, Four loop twist two, BFKL, wrapping and strings, Nucl. Phys. B 816 (2009) 376 [arXiv:0811.4448] [INSPIRE].
T. Lukowski, A. Rej and V. Velizhanin, Five-loop anomalous dimension of twist-two operators, Nucl. Phys. B 831 (2010) 105 [arXiv:0912.1624] [INSPIRE].
N. Gromov, V. Kazakov, A. Kozak and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory: TBA and excited states, Lett. Math. Phys. 91 (2010) 265 [arXiv:0902.4458] [INSPIRE].
D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [INSPIRE].
G. Arutyunov and S. Frolov, Thermodynamic Bethe ansatz for the AdS 5 × S 5 mirror model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Solving the AdS/CFT Y-system, JHEP 07 (2012) 023 [arXiv:1110.0562] [INSPIRE].
J. Balog and A. Hegedus, Hybrid-NLIE for the AdS/CFT spectral problem, JHEP 08 (2012) 022 [arXiv:1202.3244] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for AdS 5 /CFT 4, arXiv:1305.1939 [INSPIRE].
A. Kotikov and V. Velizhanin, Analytic continuation of the Mellin moments of deep inelastic structure functions, hep-ph/0501274 [INSPIRE].
T. Jaroszewicz, Gluonic Regge singularities and anomalous dimensions in QCD, Phys. Lett. B 116 (1982) 291 [INSPIRE].
B. Basso, Scaling dimensions at small spin in N = 4 SYM theory, arXiv:1205.0054 [INSPIRE].
A.V. Kotikov, A. Rej and S. Zieme, Analytic three-loop solutions for N = 4 SYM twist operators, Nucl. Phys. B 813 (2009) 460 [arXiv:0810.0691] [INSPIRE].
M. Beccaria, A. Belitsky, A. Kotikov and S. Zieme, Analytic solution of the multiloop Baxter equation, Nucl. Phys. B 827 (2010) 565 [arXiv:0908.0520] [INSPIRE].
J. Blumlein and S. Kurth, Harmonic sums and Mellin transforms up to two loop order, Phys. Rev. D 60 (1999) 014018 [hep-ph/9810241] [INSPIRE].
N. Gromov, On the derivation of the exact slope function, JHEP 02 (2013) 055 [arXiv:1205.0018] [INSPIRE].
S.E. Derkachov, G. Korchemsky and A. Manashov, Evolution equations for quark gluon distributions in multicolor QCD and open spin chains, Nucl. Phys. B 566 (2000) 203 [hep-ph/9909539] [INSPIRE].
H. De Vega and L. Lipatov, Interaction of reggeized gluons in the Baxter-Sklyanin representation, Phys. Rev. D 64 (2001) 114019 [hep-ph/0107225] [INSPIRE].
N. Gromov and V. Kazakov, private communication.
N. Gromov, Quantum spectral curve at work, talk at IGST, Utrecht The Netherlands August 19-23 2013.
S.E. Derkachov, G. Korchemsky and A. Manashov, Separation of variables for the quantum SL(2, \( \mathbb{R} \)) spin chain, JHEP 07 (2003) 047 [hep-th/0210216] [INSPIRE].
R. Frassek, T. Lukowski, C. Meneghelli and M. Staudacher, Baxter operators and Hamiltonians for ‘nearly all’ integrable closed gl(n) spin chains, arXiv:1112.3600 [INSPIRE].
G. Korchemsky, J. Kotanski and A. Manashov, Multi-reggeon compound states and resummed anomalous dimensions in QCD, Phys. Lett. B 583 (2004) 121 [hep-ph/0306250] [INSPIRE].
S.E. Derkachov, G. Korchemsky, J. Kotanski and A. Manashov, Noncompact Heisenberg spin magnets from high-energy QCD. 2. Quantization conditions and energy spectrum, Nucl. Phys. B 645 (2002) 237 [hep-th/0204124] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1309.2844
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Janik, R.A. Twist-two operators and the BFKL regime — nonstandard solutions of the Baxter equation. J. High Energ. Phys. 2013, 153 (2013). https://doi.org/10.1007/JHEP11(2013)153
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2013)153