Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2010, Article ID 103630, 43 pages
http://dx.doi.org/10.1155/2010/103630
Review Article

Holographic Renormalization of Two-Point Functions in Non-AdS/Non-CFT

1Department für Physik, Arnold Sommerfeld Zentrum für Theoretische Physik, Ludwig-Maximilians-Universität, Theresienstrasse 37, 80333 München, Germany
2Dipartimento di Scienze Fisiche, Università di Napoli “Federico II” and INFN, Sezione di Napoli, Via Cintia, 80126 Napoli, Italy

Received 19 April 2010; Accepted 14 September 2010

Academic Editor: Leopoldo P. Zayas

Copyright © 2010 Michael Haack and Wolfgang Mück. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. M. Maldacena, “The large n limit of superconformal field theories and supergravity,” Advances in Theoretical and Mathematical Physics, vol. 2, pp. 231–252, 1998. View at Google Scholar
  2. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Physics Letters B, vol. 428, no. 1-2, pp. 105–114, 1998. View at Google Scholar · View at Scopus
  3. E. Witten, “Anti-de Sitter space and holography,” Advances in Theoretical and Mathematical Physics, vol. 2, pp. 253–291, 1998. View at Google Scholar
  4. M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions, Dover Publications, New York, NY, USA, 1965.
  5. M. Henningson and K. Skenderis, “The holographic Weyl anomaly,” Journal of High Energy Physics, vol. 2, no. 7, article 023, 1998. View at Google Scholar · View at Scopus
  6. V. Balasubramanian and P. Kraus, “A stress tensor for anti-de Sitter gravity,” Communications in Mathematical Physics, vol. 208, no. 2, pp. 413–428, 1999. View at Google Scholar · View at Scopus
  7. J. de Boer, E. Verlinde, and H. Verlinde, “On the holographic renormalization group,” Journal of High Energy Physics, vol. 4, no. 8, pp. 1–15, 2000. View at Google Scholar · View at Scopus
  8. S. de Haro, K. Skenderis, and S. N. Solodukhin, “Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence,” Communications in Mathematical Physics, vol. 217, no. 3, pp. 595–622, 2001. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Kalkkinen, D. Martelli, and W. Mück, “Holographic renormalisation and anomalies,” Journal of High Energy Physics, vol. 5, no. 4, 2001. View at Google Scholar
  10. M. Bianchi, D. Z. Freedman, and K. Skenderis, “Holographic renormalization,” Nuclear Physics B, vol. 631, no. 1-2, pp. 159–194, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Martelli and W. Mück, “Holographic renormalization and Ward identities with the Hamilton-Jacobi method,” Nuclear Physics B, vol. 654, no. 1-2, pp. 248–276, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Skenderis, “Lecture notes on holographic renormalization,” Classical and Quantum Gravity, vol. 19, no. 22, pp. 5849–5876, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. I. Papadimitriou and K. Skenderis, “AdS/CFT correspondence and geometry,” http://arxiv.org/abs/hep-th/0404176.
  14. I. Papadimitriou and K. Skenderis, “Correlation functions in holographic RG flows,” Journal of High Energy Physics, vol. 8, no. 10, pp. 2531–2567, 2004. View at Google Scholar · View at Scopus
  15. K. Skenderis and B. C. V. Rees, “Real-time gauge/gravity duality: prescription, renormalization and examples,” Journal of High Energy Physics, vol. 2009, no. 5, article 085, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Taylor, “Non-relativistic holography,” http://arxiv.org/abs/0812.0530.
  17. M. Guica, K. Skenderis, M. Taylor, and B. van Rees, “Holography for Schrodinger backgrounds,” http://arxiv.org/abs/1008.1991.
  18. S. F. Ross and O. Saremi, “Holographic stress tensor for non-relativistic theories,” Journal of High Energy Physics, vol. 2009, no. 9, article 009, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. K. Balasubramanian and J. McGreevy, “An analytic Lifshitz black hole,” Physical Review D, vol. 80, no. 10, Article ID 104039, 2009. View at Publisher · View at Google Scholar
  20. P. Horava and C. M. Melby-Thompson, “Anisotropic Conformal Infinity,” http://arxiv.org/abs/0909.3841.
  21. A. Karch, A. O'Bannon, and K. Skenderis, “Holographic renormalization of probe D-branes in AdS/CFT,” Journal of High Energy Physics, vol. 2006, no. 4, pp. 349–371, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. I. Kanitscheider, K. Skenderis, and M. Taylor, “Precision holography for non-conformal branes,” Journal of High Energy Physics, vol. 2008, no. 9, article 094, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. D. Z. Freedman, C. Núñez, M. Schnabl, and K. Skenderis, “Fake supergravity and domain wall stability,” Physical Review D, vol. 69, no. 10, Article ID 104027, 2004. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Celi, A. Ceresole, G. Dall'Agata, A. Van Proeyen, and M. Zagermann, “On the fakeness of fake supergravity,” Physical Review D, vol. 71, no. 4, Article ID 045009, 16 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. M. Zagermann, “N=4 “fake” supergravity,” Physical Review D, vol. 71, no. 12, Article ID 125007, 2005. View at Publisher · View at Google Scholar
  26. O. Aharony, “The non-AdS/non-CFT correspondence, or three different paths to QCD,” http://arxiv.org/abs/hep-th/0212193.
  27. A. Zaffaroni, “RTN lectures on the non AdS / non CFT correspondence,” PoS RTN2005(2005) 005.
  28. J. Erdmenger, N. Evans, I. Kirsch, and E. J. Threlfall, “Mesons in gauge/gravity duals,” The European Physical Journal A, vol. 35, no. 1, pp. 81–133, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. N. Borodatchenkova, M. Haack, and W. Mück, “Towards holographic renormalization of fake supergravity,” Nuclear Physics B, vol. 815, no. 1-2, pp. 215–239, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. O. Aharony, A. Buchel, and A. Yarom, “Holographic renormalization of cascading gauge theories,” Physical Review D, vol. 72, no. 6, Article ID 066003, 30 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  31. M. Bianchi, M. Prisco, and W. Mück, “New results on holographic three-point functions,” Journal of High Energy Physics, vol. 7, no. 11, pp. 1163–1186, 2003. View at Google Scholar · View at Scopus
  32. W. Mück, “Progress on holographic three-point functions,” Fortschritte der Physik, vol. 53, no. 7-8, pp. 948–954, 2005. View at Publisher · View at Google Scholar · View at Scopus
  33. M. Berg, M. Haack, and W. Mück, “Bulk dynamics in confining gauge theories,” Nuclear Physics B, vol. 736, no. 1-2, pp. 82–132, 2006. View at Publisher · View at Google Scholar · View at Scopus
  34. I. R. Klebanov and M. J. Strassler, “Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities,” Journal of High Energy Physics, vol. 4, no. 8, pp. 21–35, 2000. View at Google Scholar · View at Scopus
  35. I. R. Klebanov and A. A. Tseytlin, “Gravity duals of supersymmetric SU(N)×SU(N+M) gauge theories,” Nuclear Physics B, vol. 578, no. 1-2, pp. 123–138, 2000. View at Google Scholar · View at Scopus
  36. G. Papadopoulos and A. A. Tseytlin, “Complex geometry of conifolds and a 5-brane wrapped on a 2-sphere,” Classical and Quantum Gravity, vol. 18, no. 7, pp. 1333–1353, 2001. View at Publisher · View at Google Scholar · View at Scopus
  37. D. Cassani and A. F. Faedo, “A supersymmetric consistent truncation for conifold solutions,” http://arxiv.org/abs/1008.0883.
  38. I. Bena, G. Giecold, M. Grana, N. Halmagyi, and F. Orsi, “Supersymmetric consistent truncations of IIB on T(1,1),” http://arxiv.org/abs/1008.0983.
  39. M. Krasnitz, “A two point function in a cascading N = 1 gauge theory from supergravity,” http://arxiv.org/abs/hep-th/0011179.
  40. M. Krasnitz, “Correlation functions in a cascading N=1 gauge theory,” Journal of High Energy Physics, vol. 6, no. 12, pp. 987–1015, 2002. View at Google Scholar · View at Scopus
  41. O. Aharony, A. Buchel, and A. Yarom, “Short distance properties of cascading gauge theories,” Journal of High Energy Physics, vol. 2006, no. 11, article no. 069, 2006. View at Publisher · View at Google Scholar · View at Scopus
  42. M. Mia, K. Dasgupta, C. Gale, and S. Jeon, “Five easy pieces: the dynamics of quarks in strongly coupled plasmas,” Nuclear Physics B, vol. 839, no. 1-2, pp. 187–293, 2010. View at Publisher · View at Google Scholar
  43. E. Cáceres and R. Hernández, “Glueball masses for the deformed conifold theory,” Physics Letters B, vol. 504, no. 1-2, pp. 64–70, 2001. View at Publisher · View at Google Scholar · View at Scopus
  44. E. Cáceres and X. Amador, “Spin two glueball mass and glueball regge trajectory from supergravity,” Journal of High Energy Physics, vol. 8, no. 11, pp. 627–638, 2004. View at Google Scholar · View at Scopus
  45. M. Berg, M. Haack, and W. Mück, “Glueballs vs. gluinoballs: fluctuation spectra in non-AdS/non-CFT,” Nuclear Physics B, vol. 789, no. 1-2, pp. 1–44, 2008. View at Publisher · View at Google Scholar · View at Scopus
  46. M. K. Benna, A. Dymarsky, I. R. Klebanov, and A. Solovyov, “On normal modes of a warped throat,” Journal of High Energy Physics, vol. 2008, no. 6, article 070, 2008. View at Publisher · View at Google Scholar
  47. A. Dymarsky, D. Melnikov, and A. Solovyov, “I-odd sector of the Klebanov-Strassler theory,” Journal of High Energy Physics, vol. 2009, no. 5, article 105, 2009. View at Publisher · View at Google Scholar · View at Scopus
  48. J. Maldacena and C. Nuñez, “Towards the large N limit of pure N = 1 super Yang-Mills theory,” Physical Review Letters, vol. 86, no. 4, pp. 588–591, 2001. View at Publisher · View at Google Scholar · View at Scopus
  49. V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus,” Nuclear Physics B, vol. 229, no. 2, pp. 381–393, 1983. View at Google Scholar · View at Scopus
  50. C. Núñez, I. Papadimitriou, and M. Piai, “Walking dynamics from string duals,” International Journal of Modern Physics A, vol. 25, no. 14, pp. 2837–2865, 2010. View at Publisher · View at Google Scholar
  51. O. C. Gürdoǧan, “Walking solutions in the string background dual to N = 1 SQCD-like theories,” Annals of Physics, vol. 325, no. 3, pp. 535–547, 2010. View at Publisher · View at Google Scholar
  52. M. Piai, “Lectures on walking technicolor, holography and gauge/gravity dualities,” http://arxiv.org/abs/1004.0176.
  53. T. Appelquist, D. Karabali, and L. C. R. Wijewardhana, “Chiral hierarchies and flavor-changing neutral currents in hypercolor,” Physical Review Letters, vol. 57, no. 8, pp. 957–960, 1986. View at Publisher · View at Google Scholar · View at Scopus
  54. D. Elander, C. Núñez, and M. Piai, “A light scalar from walking solutions in gauge-string duality,” Physics Letters B, vol. 686, no. 1, pp. 64–67, 2010. View at Publisher · View at Google Scholar
  55. D. Elander, “Glueball spectra of SQCD-like theories,” Journal of High Energy Physics, vol. 2010, no. 3, article 114, 2010. View at Publisher · View at Google Scholar
  56. L. Girardello, M. Petrini, M. Porrati, and A. Zaffaroni, “Novel local CFT and exact results on perturbations of N=4 super Yang Mills from AdS dynamics,” Journal of High Energy Physics, vol. 2, no. 12, article 022, 1998. View at Google Scholar · View at Scopus
  57. D. Z. Freedman, S. S. Gubser, K. Pilch, and N. P. Warner, “Continuous distributions of D3-branes and gauged supergravity,” Journal of High Energy Physics, vol. 4, no. 7, pp. 1–17, 2000. View at Google Scholar · View at Scopus
  58. A. Brandhuber and K. Sfetsos, “Wilson loops from multicentre and rotating branes, mass gaps and phase structure in gauge theories,” Advances in Theoretical and Mathematical Physics, vol. 3, pp. 851–887, 1999. View at Google Scholar
  59. O. DeWolfe and D. Z. Freedman, “Notes on fluctuations and correlation functions in holographic renormalization group flows,” http://arxiv.org/abs/hep-th/0002226.
  60. G. Arutyunov, S. Frolov, and S. Theisen, “Gravity-scalar fluctuations in holographic RG flow geometries,” Physics Letters B, vol. 484, no. 3-4, pp. 295–305, 2000. View at Publisher · View at Google Scholar · View at Scopus
  61. W. Mück, “Correlation functions in holographic renormalization group flows,” Nuclear Physics B, vol. 620, no. 3, pp. 477–500, 2002. View at Publisher · View at Google Scholar · View at Scopus
  62. R. M. Wald, General Relativity, University of Chicago Press, Chicago, Ill, USA, 1984.
  63. A. Z. Petrov, Einstein Spaces, Pergamon Press, Oxford, UK, 1969.
  64. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, Freeman, San Francisco, Calif, USA, 1973.
  65. M. Bianchi, O. DeWolfe, D. Z. Freedman, and K. Pilch, “Anatomy of two holographic renormalization group flows,” Journal of High Energy Physics, vol. 5, no. 1, article 021, 2001. View at Google Scholar · View at Scopus
  66. W. Mück and M. Prisco, “Glueball scattering amplitudes from holography,” Journal of High Energy Physics, vol. 8, no. 4, pp. 835–869, 2004. View at Google Scholar · View at Scopus
  67. M. Blanchi, “How to go with an RG Flow,” Journal of High Energy Physics, vol. 5, no. 8, article 041, 2001. View at Google Scholar
  68. S. S. Gubser, I. R. Klebanov, and C. P. Herzog, “Symmetry breaking and axionic strings in the warped deformed conifold,” Journal of High Energy Physics, vol. 8, no. 9, pp. 795–820, 2004. View at Google Scholar · View at Scopus
  69. S. S. Gubser, C. P. Herzog, and I. R. Klebanov, “Variations on the warped deformed conifold,” Comptes Rendus Physique, vol. 5, no. 9-10, pp. 1031–1038, 2004. View at Publisher · View at Google Scholar · View at Scopus
  70. A. Loewy and J. Sonnenschein, “On the holographic duals of N = 1 gauge dynamics,” Journal of High Energy Physics, vol. 5, no. 8, article 007, 2001. View at Google Scholar · View at Scopus