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OPE in planar QCD from integrability

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Abstract

We consider the operator product expansion of local gauge-invariant singletrace operators composed of self-dual components of the field strength tensor in planar QCD. Using the integrability of the 1-loop dilatation operator, we obtain a determinant expression for certain tree-level structure constants.

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References

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  3. N. Beisert and M. Staudacher, Long-range PSU (2, 2|4) Bethe ansatze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. G. Ferretti, R. Heise and K. Zarembo, New integrable structures in large-N QCD, Phys. Rev. D 70 (2004) 074024 [hep-th/0404187] [INSPIRE].

    ADS  Google Scholar 

  6. A. Zamolodchikov and V. Fateev, Model factorized S matrix and an integrable Heisenberg chain with spin. 1 (in Russian), Sov. J. Nucl. Phys. 32 (1980) 298 [INSPIRE].

    MathSciNet  Google Scholar 

  7. P. Kulish, N.Y. Reshetikhin and E. Sklyanin, Yang-Baxter equation and representation theory. 1, Lett. Math. Phys. 5 (1981) 393 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. P. Kulish and E. Sklyanin, Quantum spectral transform method. Recent developments, Lect. Notes Phys. 151 (1982) 61.

    Article  MathSciNet  ADS  Google Scholar 

  9. L. Takhtajan, The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins, Phys. Lett. A 87 (1982) 479 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. H.M. Babujian, Exact solution of the isotropic Heisenberg chain with arbitrary spins: thermodynamics of the model, Nucl. Phys. B 215 (1983) 317 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large-N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  15. J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring three-point functions and integrability, JHEP 09 (2011) 028 [arXiv:1012.2475] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. O. Foda, N = 4 SYM structure constants as determinants, JHEP 03 (2012) 096 [arXiv:1111.4663] [INSPIRE].

    ADS  Google Scholar 

  17. N. Beisert, G. Ferretti, R. Heise and K. Zarembo, One-loop QCD spin chain and its spectrum, Nucl. Phys. B 717 (2005) 137 [hep-th/0412029] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. V. Braun, G. Korchemsky and D. Mueller, The uses of conformal symmetry in QCD, Prog. Part. Nucl. Phys. 51 (2003) 311 [hep-ph/0306057] [INSPIRE].

    Article  ADS  Google Scholar 

  19. R. Jaffe and X.-D. Ji, Chiral odd parton distributions and Drell-Yan processes, Nucl. Phys. B 375 (1992) 527 [INSPIRE].

    Article  ADS  Google Scholar 

  20. V.M. Braun, S.E. Derkachov and A. Manashov, Integrability of three particle evolution equations in QCD, Phys. Rev. Lett. 81 (1998) 2020 [hep-ph/9805225] [INSPIRE].

    Article  ADS  Google Scholar 

  21. V.M. Braun, S.E. Derkachov, G. Korchemsky and A. Manashov, Baryon distribution amplitudes in QCD, Nucl. Phys. B 553 (1999) 355 [hep-ph/9902375] [INSPIRE].

    Article  ADS  Google Scholar 

  22. A.V. Belitsky, Fine structure of spectrum of twist — Three operators in QCD, Phys. Lett. B 453 (1999) 59 [hep-ph/9902361] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. C. Ahn, R.I. Nepomechie and J. Suzuki, The QCD spin chain S matrix, Nucl. Phys. B 798 (2008) 402 [arXiv:0711.2415] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. A. Belitsky, G. Korchemsky and D. Mueller, Integrability of two-loop dilatation operator in gauge theories, Nucl. Phys. B 735 (2006) 17 [hep-th/0509121] [INSPIRE].

    Article  ADS  Google Scholar 

  25. N. Gromov and P. Vieira, Quantum integrability for three-point functions, arXiv:1202.4103 [INSPIRE].

  26. A. Lima-Santos, Bethe ansatz for nineteen vertex models, J. Phys. A 32 (1999) 1819 [hep-th/9807219] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. N. Crampé, E. Ragoucy and L. Alonzi, Coordinate Bethe ansatz for spin s XXX model, SIGMA 7 (2011) 6 [arXiv:1009.0408].

    Google Scholar 

  28. A. Ovchinnikov, Coordinate space wave function from the algebraic Bethe ansatz for the inhomogeneous six-vertex model, Phys. Lett. A 374 (2010) 1311 [arXiv:1001.2672] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. A.G. Izergin, Partition function of the six-vertex model in a finite volume, Sov. Phys. Dokl. 32 (1987) 878.

    ADS  MATH  Google Scholar 

  30. V. Korepin, Calculation of norms of Bethe wave functions, Commun. Math. Phys. 86 (1982) 391 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. V. Korepin, N. Bogoliubov, and A. Izergin, Quantum inverse scattering method and correlation functions, Cambridge University Press, Cambridge U.K. (1993).

    Book  MATH  Google Scholar 

  32. N. Slavnov, Calculation of scalar products of wave functions and form factors in the framework of the algebraic Bethe ansatz, Theor. Math. Phys. 79 (1989) 502.

    Article  MathSciNet  Google Scholar 

  33. M. Gaudin, Diagonalisation of a class of spin hamiltonians, J. Phys-Paris 37 (1976) 1087.

    Article  MathSciNet  Google Scholar 

  34. M. Gaudin, B.M. McCoy and T.T. Wu, Normalization sum for the Bethe’s hypothesis wave functions of the Heisenberg-Ising chain, Phys. Rev. D 23 (1981) 417.

    MathSciNet  ADS  Google Scholar 

  35. N. Kitanine, J. Maillet and V. Terras, Form factors of the XXZ Heisenberg spin/2 finite chain, Nucl. Phys. B 554 (1999) 647 [math-ph/9807020].

    Article  MathSciNet  ADS  Google Scholar 

  36. M. Wheeler, An Izergin-Korepin procedure for calculating scalar products in six-vertex models, Nucl. Phys. B 852 (2011) 468 [arXiv:1104.2113] [INSPIRE].

    Article  ADS  Google Scholar 

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Correspondence to Rafael I Nepomechie.

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ArXiv ePrint: 1202.6553

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Ahn, C., Foda, O. & Nepomechie, R.I. OPE in planar QCD from integrability. J. High Energ. Phys. 2012, 168 (2012). https://doi.org/10.1007/JHEP06(2012)168

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  • DOI: https://doi.org/10.1007/JHEP06(2012)168

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