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The two-loop dilatation operator of \( \mathcal{N} = {4} \) super Yang-Mills theory in the SO(6) sector

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Abstract

The dilatation operator of planar \( \mathcal{N} = {4} \) super Yang-Mills in the pure scalar SO(6) sector is derived at the two-loop order. Representation theory allows for eight free coefficients in an ansatz for the corresponding spin-chain hamiltonian acting on three adjacent scalar states. While four out of these follow from the known SU(2|3) sector two-loop dilatation operator, the remaining four coefficients are derived by diagrammatic techniques and a match to the known dimension of a length three primary operator. Finally, comments upon the use of this result for the evaluation of three-point structure functions of scalar operators at the one-loop order are given.

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References

  1. N. Beisert, C. Kristjansen and M. Staudacher, The Dilatation operator of conformal \( \mathcal{N} = {4} \) super Yang-Mills theory, Nucl. Phys. B 664 (2003) 131 [hep-th/0303060] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  2. N. Beisert et al., Review of AdS/CFT Integrability: An Overview, arXiv:1012.3982 [INSPIRE].

  3. J. Minahan and K. Zarembo, The Bethe ansatz for \( \mathcal{N} = {4} \) super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  4. A. Rej, Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains, arXiv:1012.3985 [INSPIRE].

  5. L. Lipatov, High-energy asymptotics of multicolor QCD and exactly solvable lattice models, hep-th/9311037 [INSPIRE].

  6. L. Faddeev and G. Korchemsky, High-energy QCD as a completely integrable model, Phys. Lett. B 342 (1995) 311 [hep-th/9404173] [INSPIRE].

    ADS  Google Scholar 

  7. A. Belitsky, V. Braun, A. Gorsky and G. Korchemsky, Integrability in QCD and beyond, Int. J. Mod. Phys. A 19 (2004) 4715 [hep-th/0407232] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  8. G. Korchemsky, Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and \( \mathcal{N} < {4} \) SYM,arXiv:1012.4000 [INSPIRE].

  9. N. Beisert and M. Staudacher, The \( \mathcal{N} = {4} \) SYM integrable super spin chain, Nucl. Phys. B 670 (2003) 439 [hep-th/0307042] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  10. J.A. Minahan, Higher loops beyond the SU(2) sector, JHEP 10 (2004) 053 [hep-th/0405243] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. N. Beisert, V. Kazakov and K. Sakai, Algebraic curve for the SO(6) sector of AdS/CFT, Commun. Math. Phys. 263 (2006) 611 [hep-th/0410253] [INSPIRE].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. N. Beisert, The SU(2|3) dynamic spin chain, Nucl. Phys. B 682 (2004) 487 [hep-th/0310252] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  13. C. Sieg, Superspace computation of the three-loop dilatation operator of \( \mathcal{N} = {4} \) SYM theory, Phys. Rev. D 84 (2011) 045014 [arXiv:1008.3351] [INSPIRE].

    ADS  Google Scholar 

  14. B. Eden, A Two-loop test for the factorised S-matrix of planar \( \mathcal{N} = {4} \), Nucl. Phys. B 738 (2006) 409 [hep-th/0501234] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  15. B. Eden, C. Jarczak and E. Sokatchev, Three-loop test of the dilatation operator and integrability in = 4 SYM, Fortsch. Phys. 53 (2005) 610.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. C. Sieg, Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory, arXiv:1012.3984 [INSPIRE].

  17. A. Belitsky, J. Henn, C. Jarczak, D. Müller and E. Sokatchev, Anomalous dimensions of leading twist conformal operators, Phys. Rev. D 77 (2008) 045029 [arXiv:0707.2936] [INSPIRE].

    ADS  Google Scholar 

  18. N. Beisert, C. Kristjansen, J. Plefka, G. Semenoff and M. Staudacher, BMN correlators and operator mixing in \( \mathcal{N} = {4} \) super Yang-Mills theory, Nucl. Phys. B 650 (2003) 125 [hep-th/0208178] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  19. R. Roiban and A. Volovich, Yang-Mills correlation functions from integrable spin chains, JHEP 09 (2004) 032 [hep-th/0407140] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. K. Okuyama and L.-S. Tseng, Three-point functions in \( \mathcal{N} = {4} \) SYM theory at one-loop, JHEP 08 (2004) 055 [hep-th/0404190] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  21. L.F. Alday, J.R. David, E. Gava and K. Narain, Structure constants of planar \( \mathcal{N} = {4} \) Yang-Mills at one loop, JHEP 09 (2005) 070 [hep-th/0502186] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  22. L.F. Alday, J.R. David, E. Gava and K. Narain, Towards a string bit formulation of \( \mathcal{N} = {4} \) super Yang-Mills, JHEP 04 (2006) 014 [hep-th/0510264] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  23. G. Georgiou, V.L. Gili and R. Russo, Operator mixing and three-point functions in \( \mathcal{N} = {4} \) SYM, JHEP 10 (2009) 009 [arXiv:0907.1567] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  24. K. Zarembo, Holographic three-point functions of semiclassical states, JHEP 09 (2010) 030 [arXiv:1008.1059] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  25. M.S. Costa, R. Monteiro, J.E. Santos and D. Zoakos, On three-point correlation functions in the gauge/gravity duality, JHEP 11 (2010) 141 [arXiv:1008.1070] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  26. R. Roiban and A. Tseytlin, On semiclassical computation of 3-point functions of closed string vertex operators in AdS5 × S5, Phys. Rev. D 82 (2010) 106011 [arXiv:1008.4921] [INSPIRE].

    ADS  Google Scholar 

  27. R. Hernandez, Three-point correlation functions from semiclassical circular strings, J. Phys. A 44 (2011) 085403 [arXiv:1011.0408] [INSPIRE].

    ADS  Google Scholar 

  28. G. Georgiou, Two and three-point correlators of operators dual to folded string solutions at strong coupling, JHEP 02 (2011) 046 [arXiv:1011.5181] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  29. C. Park and B.-H. Lee, Correlation functions of magnon and spike, Phys. Rev. D 83 (2011) 126004 [arXiv:1012.3293] [INSPIRE].

    ADS  Google Scholar 

  30. D. Bak, B. Chen and J.-B. Wu, Holographic Correlation Functions for Open Strings and Branes, JHEP 06 (2011) 014 [arXiv:1103.2024] [INSPIRE].

    Article  ADS  Google Scholar 

  31. A. Bissi, C. Kristjansen, D. Young and K. Zoubos, Holographic three-point functions of giant gravitons, JHEP 06 (2011) 085 [arXiv:1103.4079] [INSPIRE].

    Article  ADS  Google Scholar 

  32. R. Hernandez, Three-point correlators for giant magnons, JHEP 05 (2011) 123 [arXiv:1104.1160] [INSPIRE].

    Article  ADS  Google Scholar 

  33. C. Ahn and P. Bozhilov, Three-point Correlation functions of Giant magnons with finite size, Phys. Lett. B 702 (2011) 286 [arXiv:1105.3084] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  34. J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring Three-Point Functions and Integrability, JHEP 09 (2011) 028 [arXiv:1012.2475] [INSPIRE].

    Article  ADS  Google Scholar 

  35. J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match, JHEP 09 (2011) 029 [arXiv:1104.5501] [INSPIRE].

    Article  ADS  Google Scholar 

  36. C. Kristjansen, Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity, arXiv:1012.3997 [INSPIRE].

  37. A. Grossardt and J. Plefka, One-Loop Spectroscopy of Scalar Three-Point Functions in planar \( \mathcal{N} = {4} \) super Yang-Mills Theory, arXiv:1007.2356 [INSPIRE].

  38. G. Georgiou, V.L. Gili and J. Plefka, One-Loop Three-Point Functions in planar N = 4 super Yang-Mills Theory for Scalar Operators up to Length Five, in preparation.

  39. N. Beisert, The Dilatation operator of \( \mathcal{N} = {4} \) super Yang-Mills theory and integrability, Phys. Rept. 405 (2005) 1 [hep-th/0407277] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  40. G. Georgiou, V.L. Gili and R. Russo, Operator Mixing and the AdS/CFT correspondence, JHEP 01 (2009) 082 [arXiv:0810.0499] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  41. Z. Xiao, BMN operators with a scalar fermion pair and operator mixing in \( \mathcal{N} = {4} \) Super Yang-Mills Theory, Phys. Rev. D 81 (2010) 026004 [arXiv:0910.3390] [INSPIRE].

    ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Demokritos National Research Center, Institute of Nuclear Physics, Ag. Paraskevi, GR-15310, Athens, Greece

    George Georgiou

  2. Centre for Research in String Theory, School of Physics, Queen Mary University of London, Mile End Road, London, E14NS, United Kingdom

    Valeria Gili

  3. Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489, Berlin, Germany

    Jan Plefka

  4. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106 - 4030, USA

    Jan Plefka

Authors
  1. George Georgiou
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  2. Valeria Gili
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  3. Jan Plefka
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Correspondence to Valeria Gili.

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ArXiv ePrint: 1106.0724

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Georgiou, G., Gili, V. & Plefka, J. The two-loop dilatation operator of \( \mathcal{N} = {4} \) super Yang-Mills theory in the SO(6) sector. J. High Energ. Phys. 2011, 75 (2011). https://doi.org/10.1007/JHEP12(2011)075

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