Skip to main content
SpringerLink
Log in

Semiclassical Strings and AdS/CFT

  • Conference paper
String Theory: From Gauge Interactions to Cosmology

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry ((NAII,volume 208))

Abstract

We discuss AdS/CFT duality in the sector of “semiclassical” string states with large quantum numbers. We review the coherent-state effective action approach, in which similar 2d sigma model actions appear from the AdS 5 × S 5 string action and from the integrable spin chain Hamiltonian representing the N=4 super Yang-Mills dilatation operator. We consider mostly the leading-order terms in the energies/anomalous dimensions which match but comment also on higher-order corrections.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [hep-th/9711200].

    MATH  MathSciNet  ADS  Google Scholar 

  2. S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428, 105 (1998) [hep-th/9802109].

    Article  MathSciNet  ADS  Google Scholar 

  3. E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253 (1998) [hep-th/9802150].

    MATH  MathSciNet  Google Scholar 

  4. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large N field theories, string theory and gravity,” Phys. Rept. 323, 183 (2000) [hep-th/9905111]. I. R. Klebanov, “TASI lectures: Introduction to the AdS/CFT correspondence,” hep-th/0009139.

    Article  MathSciNet  ADS  Google Scholar 

  5. A. M. Polyakov, “Gauge fields and space-time,” Int. J. Mod. Phys. A 17S1, 119 (2002) [hep-th/0110196].

    Article  MathSciNet  Google Scholar 

  6. D. Berenstein, J. M. Maldacena and H. Nastase, “Strings in flat space and pp waves from N =4 super Yang Mills,” JHEP 0204, 013 (2002) [hep-th/0202021].

    Article  MathSciNet  ADS  Google Scholar 

  7. R. R. Metsaev and A. A. Tseytlin, “Type IIB superstring action in AdS 5 × S 5 background,” Nucl. Phys. B 533, 109 (1998) [hep-th/9805028].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “A semi-classical limit of the gauge/string correspondence,” Nucl. Phys. B 636, 99 (2002) [hep-th/0204051].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. M. Blau, J. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, “A new maximally supersymmetric background of IIB superstring theory,” JHEP 0201, 047 (2002) [hep-th/0110242].

    Article  MathSciNet  ADS  Google Scholar 

  10. R. R. Metsaev, “Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background,” Nucl. Phys. B 625, 70 (2002) [hep-th/0112044]. R. R. Metsaev and A. A. Tseytlin, “Exactly solvable model of superstring in plane wave Ramond-Ramond background,” Phys. Rev. D 65, 126004 (2002) [hep-th/0202109].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. S. Frolov and A. A. Tseytlin, “Semiclassical quantization of rotating superstring in AdS 5 × S 5,” JHEP 0206, 007 (2002) [hep-th/0204226].

    Article  MathSciNet  ADS  Google Scholar 

  12. A. A. Tseytlin, “Semiclassical quantization of superstrings: AdS 5 × S 5 and beyond,” Int. J. Mod. Phys. A 18, 981 (2003) [hep-th/0209116].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. A. Parnachev and A. V. Ryzhov, “Strings in the near plane wave background and AdS/CFT,” JHEP 0210, 066 (2002) [hep-th/0208010].

    Article  MathSciNet  ADS  Google Scholar 

  14. C. G. Callan, H. K. Lee, T. McLoughlin, J. H. Schwarz, I. Swanson and X. Wu, “Quantizing string theory in AdS 5 × S 5: Beyond the pp-wave,” Nucl. Phys. B 673, 3 (2003) [hep-th/0307032]. C. G. Callan, T. McLoughlin and I. Swanson, “Holography beyond the Penrose limit,” hep-th/0404007; “Higher impurity AdS/CFT correspondence in the near-BMN limit,” hep-th/0405153.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. D. Mateos, T. Mateos and P. K. Townsend, “Supersymmetry of tensionless rotating strings in AdS 5 × S 5, and nearly-BPS operators,” hep-th/0309114. “More on supersymmetric tensionless rotating strings in AdS 5 × S 5,” hep-th/0401058.

    Google Scholar 

  16. A. Mikhailov, “Speeding strings,” JHEP 0312, 058 (2003) [hep-th/0311019].

    Article  ADS  Google Scholar 

  17. A. Mikhailov, “Slow evolution of nearly-degenerate extremal surfaces,” hep-th/0402067. “Supersymmetric null-surfaces,” hep-th/0404173.

    Google Scholar 

  18. A. Mikhailov, “Supersymmetric null-surfaces,” hep-th/0404173.

    Google Scholar 

  19. D. J. Gross, A. Mikhailov and R. Roiban, “Operators with large R charge in N = 4 Yang-Mills theory,” Annals Phys. 301, 31 (2002) [hep-th/0205066].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. N. Beisert, C. Kristjansen and M. Staudacher, “The dilatation operator of N = 4 super Yang-Mills theory,” Nucl. Phys. B 664, 131 (2003) [hep-th/0303060].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. N. Beisert, “The su(2∣3) dynamic spin chain,” hep-th/0310252.

    Google Scholar 

  22. N. Beisert, “The dilatation operator of N = 4 super Yang-Mills theory and integrability,” hep-th/0407277. “Higher-Loop Integrability in N=4 Gauge Theory,” hep-th/0409147.

    Google Scholar 

  23. B. Eden, C. Jarczak and E. Sokatchev, “A three-loop test of the dilatation operator in N = 4 SYM,” hep-th/0409009.

    Google Scholar 

  24. A. Santambrogio and D. Zanon, “Exact anomalous dimensions of N = 4 Yang-Mills operators with large R charge,” Phys. Lett. B 545, 425 (2002) [hep-th/0206079].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. J. C. Plefka, “Lectures on the plane-wave string / gauge theory duality,” Fortsch. Phys. 52, 264 (2004) [hep-th/0307101]. A. Pankiewicz, “Strings in plane wave backgrounds,” Fortsch. Phys. 51, 1139 (2003) [hep-th/0307027]. D. Sadri and M. M. Sheikh-Jabbari, “The plane-wave / super Yang-Mills duality,” hep-th/0310119.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. I. R. Klebanov, M. Spradlin and A. Volovich, “New effects in gauge theory from pp-wave superstrings,” Phys. Lett. B 548, 111 (2002) [hep-th/0206221].

    Article  ADS  MATH  Google Scholar 

  27. D. Serban and M. Staudacher, “Planar N = 4 gauge theory and the Inozemtsev long range spin chain,” JHEP 0406, 001 (2004) [hep-th/0401057].

    Article  MathSciNet  ADS  Google Scholar 

  28. N. Beisert, V. Dippel and M. Staudacher, “A novel long range spin chain and planar N = 4 super Yang-Mills,” hep-th/0405001.

    Google Scholar 

  29. G. Arutyunov, S. Frolov and M. Staudacher, “Bethe ansatz for quantum strings,” hep-th/0406256.

    Google Scholar 

  30. K. Pohlmeyer, “Integrable Hamiltonian Systems And Interactions Through Quadratic Constraints,” Commun. Math. Phys. 46, 207 (1976).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. D. J. Gross and F. Wilczek, “Asymptotically Free Gauge Theories. I,” Phys. Rev. D 8, 3633 (1973).

    Article  ADS  Google Scholar 

  32. A. V. Kotikov, L. N. Lipatov and V. N. Velizhanin, “Anomalous dimensions of Wilson operators in N = 4 SYM theory,” Phys. Lett. B 557, 114 (2003) [hep-ph/0301021].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. A. V. Kotikov, L. N. Lipatov, A. I. Onishchenko and V. N. Velizhanin, “Three-loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model,” hep-th/0404092.

    Google Scholar 

  34. S. S. Gubser, I. R. Klebanov and A. A. Tseytlin, “Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory,” Nucl. Phys. B 534, 202 (1998) [hep-th/9805156].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. S. Frolov and A. A. Tseytlin, “Multi-spin string solutions in AdS 5 × S 5,” Nucl. Phys. B 668, 77 (2003) [hep-th/0304255].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. S. Frolov and A. A. Tseytlin, “Quantizing three-spin string solution in AdS 5 × S 5,” JHEP 0307, 016 (2003) [hep-th/0306130].

    Article  MathSciNet  ADS  Google Scholar 

  37. S. Frolov and A. A. Tseytlin, “Rotating string solutions: AdS/CFT duality in nonsupersymmetric sectors,” Phys. Lett. B 570, 96 (2003) [hep-th/0306143].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. G. Arutyunov, S. Frolov, J. Russo and A. A. Tseytlin, “Spinning strings in AdS 5 × S 5 and integrable systems,” Nucl. Phys. B 671, 3 (2003) [hep-th/0307191].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. G. Arutyunov, J. Russo and A. A. Tseytlin, “Spinning strings in AdS 5 × S 5: New integrable system relations,” Phys. Rev. D 69, 086009 (2004) [hep-th/0311004].

    Article  MathSciNet  ADS  Google Scholar 

  40. A. A. Tseytlin, “Spinning strings and AdS/CFT duality,” hep-th/0311139.

    Google Scholar 

  41. J. A. Minahan and K. Zarembo, “The Bethe-ansatz for N = 4 super Yang-Mills,” JHEP 0303, 013 (2003) [hep-th/0212208].

    Article  MathSciNet  ADS  Google Scholar 

  42. N. Beisert, J. A. Minahan, M. Staudacher and K. Zarembo, “Stringing spins and spinning strings,” JHEP 0309, 010 (2003) [hep-th/0306139].

    Article  MathSciNet  ADS  Google Scholar 

  43. N. Beisert, S. Frolov, M. Staudacher and A. A. Tseytlin, “Precision spectroscopy of AdS/CFT,” JHEP 0310, 037 (2003) [hep-th/0308117].

    Article  MathSciNet  ADS  Google Scholar 

  44. G. Arutyunov and M. Staudacher, “Matching higher conserved charges for strings and spins,” JHEP 0403, 004 (2004) [hep-th/0310182]. “Two-loop commuting charges and the string / gauge duality,” hep-th/0403077.

    Article  MathSciNet  ADS  Google Scholar 

  45. J. Engquist, J. A. Minahan and K. Zarembo, “Yang-Mills duals for semiclassical strings on AdS 5 × S 5,” JHEP 0311, 063 (2003) [hep-th/0310188].

    Article  MathSciNet  ADS  Google Scholar 

  46. M. Kruczenski, “Spin chains and string theory,” hep-th/0311203.

    Google Scholar 

  47. V. A. Kazakov, A. Marshakov, J. A. Minahan and K. Zarembo, “Classical/quantum integrability in AdS/CFT,” hep-th/0402207.

    Google Scholar 

  48. M. Kruczenski, A. V. Ryzhov and A. A. Tseytlin, “Large spin limit of AdS 5 × S 5 string theory and low energy expansion of ferromagnetic spin chains,” hep-th/0403120.

    Google Scholar 

  49. M. Lubcke and K. Zarembo, “Finite-size corrections to anomalous dimensions in N = 4 SYM theory,” JHEP 0405, 049 (2004) [hep-th/0405055].

    Article  MathSciNet  ADS  Google Scholar 

  50. C. Kristjansen, “Three-spin strings on AdS 5 × S 5 from N = 4 SYM,” Phys. Lett. B 586, 106 (2004) [hep-th/0402033]. L. Freyhult, “Bethe ansatz and fluctuations in SU(3) Yang-Mills operators,” hep-th/0405167. C. Kristjansen and T. Mansson, “The Circular, Elliptic Three Spin String from the SU(3) Spin Chain,” hep-th/0406176.

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. J. A. Minahan, “Circular semiclassical string solutions on AdS 5 × S 5,” Nucl. Phys. B 648, 203 (2003) [hep-th/0209047].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  53. A. Perelomov, “Generalized Coherent States and Their Applications”, Berlin, Germany: Springer (1986) 320 p. W. M. Zhang, D. H. Feng and R. Gilmore, “Coherent States: Theory And Some Applications,” Rev. Mod. Phys. 62, 867 (1990).

    MATH  Google Scholar 

  54. E. H. Fradkin, “Field Theories Of Condensed Matter Systems,” Redwood City, USA: Addison-Wesley (1991) 350 p. (Frontiers in physics, 82). S. Sachdev, “Quantum phase transitions”, Cambridge U. Press (1999) 352 p.

    MATH  Google Scholar 

  55. R. Hernandez and E. Lopez, “The SU(3) spin chain sigma model and string theory,” JHEP 0404, 052 (2004) [hep-th/0403139].

    Article  MathSciNet  ADS  Google Scholar 

  56. B. J. Stefanski, Jr. and A. A. Tseytlin, “Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations,” JHEP 0405, 042 (2004) [hep-th/0404133].

    Article  MathSciNet  ADS  Google Scholar 

  57. M. Kruczenski and A. A. Tseytlin, “Semiclassical relativistic strings in S5 and long coherent operators in N = 4 SYM theory,” hep-th/0406189.

    Google Scholar 

  58. L. D. Faddeev and L. A. Takhtajan, “Hamiltonian Methods In The Theory Of Solitons,” Springer, Berlin (1987) 592 p. L. D. Faddeev, “How Algebraic Bethe Ansatz works for integrable model,” hep-th/9605187.

    MATH  Google Scholar 

  59. J. A. Minahan, “Higher loops beyond the SU(2) sector,” hep-th/0405243.

    Google Scholar 

  60. A. V. Ryzhov and A. A. Tseytlin, “Towards the exact dilatation operator of N = 4 super Yang-Mills theory,” hep-th/0404215.

    Google Scholar 

  61. N. Beisert, “Higher loops, integrability and the near BMN limit,” JHEP 0309, 062 (2003) [hep-th/0308074].

    Article  MathSciNet  ADS  Google Scholar 

  62. N. Beisert, “Spin chain for quantum strings,” hep-th/0409054.

    Google Scholar 

  63. A. V. Belitsky, V. M. Braun, A. S. Gorsky and G. P. Korchemsky, “Integrability in QCD and beyond,” hep-th/0407232.

    Google Scholar 

  64. A. V. Belitsky, A. S. Gorsky and G. P. Korchemsky, “Gauge / string duality for QCD conformal operators,” Nucl. Phys. B 667, 3 (2003) [hep-th/0304028].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. A. V. Belitsky, S. E. Derkachov, G. P. Korchemsky and A. N. Manashov, “Superconformal operators in N = 4 super-Yang-Mills theory,” hep-th/0311104. “Quantum integrability in (super) Yang-Mills theory on the light-cone,” hep-th/0403085.

    Google Scholar 

  66. S. A. Frolov, I. Y. Park and A. A. Tseytlin, “On one-loop correction to energy of spinning strings in S 5,” hep-th/0408187.

    Google Scholar 

  67. A. Jevicki and N. Papanicolaou, “Semiclassical Spectrum Of The Continuous Heisenberg Spin Chain,” Annals Phys. 120, 107 (1979).

    Article  ADS  Google Scholar 

  68. D. Anselmi, “The N = 4 quantum conformal algebra,” Nucl. Phys. B 541, 369 (1999) [hep-th/9809192].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  69. S. Bellucci, P. Y. Casteill, J. F. Morales and C. Sochichiu, “sl(2) spin chain and spinning strings on AdS 5 × S 5,” hep-th/0409086.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, The Ohio State University, Columbus, OH, 43210-1106, USA

    Arkady A. Tseytlin

  2. London and Lebedev Physics Institute, Imperial College, Moscow

    Arkady A. Tseytlin

Authors
  1. Arkady A. Tseytlin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Université Pierre et Marie Curie, Paris, France

    Laurent Baulieu  & Boris Pioline  & 

  2. University of Amsterdam, The Netherlands

    Jan de Boer

  3. Hebrew University, Jerusalem, Israel

    Eliezer Rabinovici

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer

About this paper

Cite this paper

Tseytlin, A.A. (2005). Semiclassical Strings and AdS/CFT. In: Baulieu, L., de Boer, J., Pioline, B., Rabinovici, E. (eds) String Theory: From Gauge Interactions to Cosmology. NATO Science Series II: Mathematics, Physics and Chemistry, vol 208. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3733-3_12

Download citation

Publish with us

Policies and ethics

Search

Navigation