On certain integrals that appear in conformal field theory

Journal of Mathematical Physics

Volumn 44, Issue 5, 2003, Pages 2293-2319

  Geronimo, Jeffrey S ^a   Navelet, Henri ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037908909     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1536020     Document Type: Article

References (27)

1. L. N. Lipatov, Sov. J. Nucl. Phys. 23, 642 (1976); V. S. Fadin, E. A. Kuraev, and L. N. Lipatov, Phys. Lett. 60B, 50 (1975); E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, Sov. Phys. JETP 44, 45 (1976); 45, 199 (1977); I. I. Balitsky and L. N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978); L. N. Lipatov, Zh. Eksp. Teor. FizRto 90, 1536 (1986) [English translation: Sov. Phys. JETP 63, 904 (1986)].
2. L. N. Lipatov, Sov. J. Nucl. Phys. 23, 642 (1976); V. S. Fadin, E. A. Kuraev, and L. N. Lipatov, Phys. Lett. 60B, 50 (1975); E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, Sov. Phys. JETP 44, 45 (1976); 45, 199 (1977); I. I. Balitsky and L. N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978); L. N. Lipatov, Zh. Eksp. Teor. FizRto 90, 1536 (1986) [English translation: Sov. Phys. JETP 63, 904 (1986)].
3. L. N. Lipatov, Sov. J. Nucl. Phys. 23, 642 (1976); V. S. Fadin, E. A. Kuraev, and L. N. Lipatov, Phys. Lett. 60B, 50 (1975); E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, Sov. Phys. JETP 44, 45 (1976); 45, 199 (1977); I. I. Balitsky and L. N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978); L. N. Lipatov, Zh. Eksp. Teor. FizRto 90, 1536 (1986) [English translation: Sov. Phys. JETP 63, 904 (1986)].
4. L. N. Lipatov, Sov. J. Nucl. Phys. 23, 642 (1976); V. S. Fadin, E. A. Kuraev, and L. N. Lipatov, Phys. Lett. 60B, 50 (1975); E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, Sov. Phys. JETP 44, 45 (1976); 45, 199 (1977); I. I. Balitsky and L. N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978); L. N. Lipatov, Zh. Eksp. Teor. FizRto 90, 1536 (1986) [English translation: Sov. Phys. JETP 63, 904 (1986)].
5. L. N. Lipatov, Sov. J. Nucl. Phys. 23, 642 (1976); V. S. Fadin, E. A. Kuraev, and L. N. Lipatov, Phys. Lett. 60B, 50 (1975); E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, Sov. Phys. JETP 44, 45 (1976); 45, 199 (1977); I. I. Balitsky and L. N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978); L. N. Lipatov, Zh. Eksp. Teor. FizRto 90, 1536 (1986) [English translation: Sov. Phys. JETP 63, 904 (1986)].
6. L. N. Lipatov, Sov. J. Nucl. Phys. 23, 642 (1976); V. S. Fadin, E. A. Kuraev, and L. N. Lipatov, Phys. Lett. 60B, 50 (1975); E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, Sov. Phys. JETP 44, 45 (1976); 45, 199 (1977); I. I. Balitsky and L. N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978); L. N. Lipatov, Zh. Eksp. Teor. FizRto 90, 1536 (1986) [English translation: Sov. Phys. JETP 63, 904 (1986)].
7. H. Navelet and R. Peschanski, Nucl. Phys. B 507, 353 (1997).
8. See, for instance, A. Bialas, H. Navelet, and R. Peschanski, "The QCD triple Pomeron coupling from string amplitudes," Saclay Preprint T97/145, hep-ph/9711442; G. P. Korchemsky, "Conformal bootstrap for the BFKL Pomeron," Orsay Preprint LPTHE 97-62 and hep-ph/9711277.
9. See, for instance, A. Bialas, H. Navelet, and R. Peschanski, "The QCD triple Pomeron coupling from string amplitudes," Saclay Preprint T97/145, hep-ph/9711442; G. P. Korchemsky, "Conformal bootstrap for the BFKL Pomeron," Orsay Preprint LPTHE 97-62 and hep-ph/9711277.
10. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
11. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
12. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
13. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
14. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
15. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
16. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
17. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
18. A. M. Polyakov, Zh. Eksp. Teor. Fiz. Lett. 12, 538 (1970); 66, 23 (1974); A. A. Migdal, Phys. Lett. 44B, 112 (1972); A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984); V. S. Dotsenko and V. A. Fateev, ibid. 240(FS12), 312 (1994). For a collection of reprints on conformal invariance, see Conformal Invariance and Applications to Statistical Mechanics, edited by C. Itzykson, H. Saleur, and J. B. Zuber (World Scientific, Singapore, 1988); Conformal Field Theory, edited by P. Di Francesco, P. Mathieu, and D. Senechal (Springer, New York, 1997); R. Guida and N. Magnoli, to be published in International J. Phys. A (see Appendices A and B); S. D. Mathur, Nucl. Phys. B 369 (1992).
19. F. W. J. Olver, Asymptotics and Special Functions (Academic, New York, 1974).
20. R. Peschanski, Phys. Lett. B 409, 49 (1997); A. H. Mueller and B. Patel, Nucl. Phys. B 425, 471 (1994); M. A. Braun and G. P. Vacca Bologna, university preprint, hep-ph/9711486; J. Bartels, Z. Phys. C 60, 471 (1993).
21. R. Peschanski, Phys. Lett. B 409, 49 (1997); A. H. Mueller and B. Patel, Nucl. Phys. B 425, 471 (1994); M. A. Braun and G. P. Vacca Bologna, university preprint, hep-ph/9711486; J. Bartels, Z. Phys. C 60, 471 (1993).
22. R. Peschanski, Phys. Lett. B 409, 49 (1997); A. H. Mueller and B. Patel, Nucl. Phys. B 425, 471 (1994); M. A. Braun and G. P. Vacca Bologna, university preprint, hep-ph/9711486; J. Bartels, Z. Phys. C 60, 471 (1993).
23. R. Peschanski, Phys. Lett. B 409, 49 (1997); A. H. Mueller and B. Patel, Nucl. Phys. B 425, 471 (1994); M. A. Braun and G. P. Vacca Bologna, university preprint, hep-ph/9711486; J. Bartels, Z. Phys. C 60, 471 (1993).
24. G. H. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, New York, 1995).
25. Y. L. Luke, Special Functions and Their Applications (Academic, New York, 1969), Vol. 1.
26. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integral and Series (Gordon and Breach, New York, 1990), Vol. 3; E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).
27. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integral and Series (Gordon and Breach, New York, 1990), Vol. 3; E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).