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On the perturbative S-matrix of generalized sine-Gordon models

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Abstract

Motivated by its relation to the Pohlmeyer reduction of AdS 5 × S 5 superstring theory we continue the investigation of the generalized sine-Gordon model defined by SO(N + 1)/SO(N) gauged WZW theory with an integrable potential. Extending our previous work (arXiv:0912.2958) we compute the one-loop two-particle S-matrix for the elementary massive excitations. In the N = 2 case corresponding to the complex sine-Gordon theory it agrees with the charge-one sector of the quantum soliton S-matrix proposed in hep-th/9410140. In the case of N > 2 when the gauge group SO(N) is non-abelian we find a curious anomaly in the Yang-Baxter equation which we interpret as a gauge artifact related to the fact that the scattered particles are not singlets under the residual global subgroup of the gauge group.

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References

  1. B. Hoare and A.A. Tseytlin, Tree-level S-matrix of Pohlmeyer reduced form of AdS 5 × S 5 superstring theory, JHEP 02 (2010) 094 [arXiv:0912.2958] [SPIRES].

    Article  ADS  Google Scholar 

  2. K. Pohlmeyer, Integrable Hamiltonian Systems and Interactions Through Quadratic Constraints, Commun. Math. Phys. 46 (1976) 207 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. I. Bakas, Conservation laws and geometry of perturbed coset models, Int. J. Mod. Phys. A 9 (1994) 3443 [hep-th/9310122] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  4. Q.-H. Park, Deformed coset models from gauged WZW actions, Phys. Lett. B 328 (1994) 329 [hep-th/9402038] [SPIRES].

    ADS  Google Scholar 

  5. T.J. Hollowood, J.L. Miramontes and Q.-H. Park, Massive integrable soliton theories, Nucl. Phys. B 445 (1995) 451 [hep-th/9412062] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. I. Bakas, Q.-H. Park and H.-J. Shin, Lagrangian Formulation of Symmetric Space sine-Gordon Models, Phys. Lett. B 372 (1996) 45 [hep-th/9512030] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  7. C.R. Fernandez-Pousa, M.V. Gallas, T.J. Hollowood and J.L. Miramontes, The symmetric space and homogeneous sine-Gordon theories, Nucl. Phys. B 484 (1997) 609 [hep-th/9606032] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. M. Grigoriev and A.A. Tseytlin, Pohlmeyer reduction of AdS 5 × S 5 superstring σ-model, Nucl. Phys. B 800 (2008) 450 [arXiv:0711.0155] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. J.L. Miramontes, Pohlmeyer reduction revisited, JHEP 10 (2008) 087 [arXiv:0808.3365] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. H.J. De Vega and N.G. Sanchez, Exact integrability of strings in D-Dimensional de Sitter space-time, Phys. Rev. D 47 (1993) 3394 [SPIRES].

    ADS  Google Scholar 

  11. A. Mikhailov, An action variable of the sine-Gordon model, J. Geom. Phys. 56 (2006) 2429 [hep-th/0504035] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. A. Mikhailov, A nonlocal Poisson bracket of the sine-Gordon model, hep-th/0511069 [SPIRES].

  13. M. Grigoriev and A.A. Tseytlin, On reduced models for superstrings on AdS n × S n, Int. J. Mod. Phys. A 23 (2008) 2107 [arXiv:0806.2623] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  14. D.M. Hofman and J.M. Maldacena, Giant magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [SPIRES].

    MathSciNet  Google Scholar 

  15. H.-Y. Chen, N. Dorey and K. Okamura, Dyonic giant magnons, JHEP 09 (2006) 024 [hep-th/0605155] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. K. Okamura and R. Suzuki, A perspective on classical strings from complex sine-Gordon solitons, Phys. Rev. D 75 (2007) 046001 [hep-th/0609026] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  17. A. Jevicki, K. Jin, C. Kalousios and A. Volovich, Generating AdS String Solutions, JHEP 03 (2008) 032 [arXiv:0712.1193] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. A. Jevicki and K. Jin, Solitons and AdS String Solutions, Int. J. Mod. Phys. A 23 (2008) 2289 [arXiv:0804.0412] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  19. T.J. Hollowood and J.L. Miramontes, Magnons, their Solitonic Avatars and the Pohlmeyer Reduction, JHEP 04 (2009) 060 [arXiv:0902.2405] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. L.F. Alday and J. Maldacena, Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space, JHEP 11 (2009) 082 [arXiv:0904.0663] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. T.J. Hollowood and J.L. Miramontes, The Relativistic Avatars of Giant Magnons and their S-matrix, JHEP 10 (2010) 012 [arXiv:1006.3667] [SPIRES].

    Article  ADS  Google Scholar 

  22. A. Mikhailov and S. Schäfer-Nameki, sine-Gordon-like action for the Superstring in AdS 5 × S 5, JHEP 05 (2008) 075 [arXiv:0711.0195] [SPIRES].

    Article  ADS  Google Scholar 

  23. R. Roiban and A.A. Tseytlin, UV finiteness of Pohlmeyer-reduced form of the AdS 5 × S 5 superstring theory, JHEP 04 (2009) 078 [arXiv:0902.2489] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. B. Hoare, Y. Iwashita and A.A. Tseytlin, Pohlmeyer-reduced form of string theory in AdS 5 × S 5 : semiclassical expansion, J. Phys. A 42 (2009) 375204 [arXiv:0906.3800] [SPIRES].

    MathSciNet  Google Scholar 

  25. Y. Iwashita, One-loop corrections to AdS 5 × S 5 superstring partition function via Pohlmeyer reduction, J. Phys. A 43 (2010) 345403 [arXiv:1005.4386] [SPIRES].

    Google Scholar 

  26. A.B. Zamolodchikov and A.B. Zamolodchikov, Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field models, Annals Phys. 120 (1979) 253 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. E. Ogievetsky, P. Wiegmann and N. Reshetikhin, The Principal Chiral Field in Two-Dimensions on Classical Lie Algebras: The Bethe Ansatz Solution and Factorized Theory of Scattering, Nucl. Phys. B 280 (1987) 45 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  28. N. Dorey and T.J. Hollowood, Quantum scattering of charged solitons in the complex sine-Gordon model, Nucl. Phys. B 440 (1995) 215 [hep-th/9410140] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. P. Dorey, Exact S matrices, in Budapest 1996, Conformal field theories and integrable models, hep-th/9810026 [SPIRES].

  30. T. Klose, T. McLoughlin, R. Roiban and K. Zarembo, Worldsheet scattering in AdS 5 × S 5, JHEP 03 (2007) 094 [hep-th/0611169] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. N. Beisert and P. Koroteev, Quantum Deformations of the One-Dimensional Hubbard Model, J. Phys. A 41 (2008) 255204 [arXiv:0802.0777] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  32. N. Beisert, The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain, arXiv:1002.1097 [SPIRES].

  33. C.R. Fernandez-Pousa and J.L. Miramontes, Semi-classical spectrum of the homogeneous sine-Gordon theories, Nucl. Phys. B 518 (1998) 745 [hep-th/9706203] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. J.L. Miramontes and C.R. Fernandez-Pousa, Integrable quantum field theories with unstable particles, Phys. Lett. B 472(2000) 392 [hep-th/9910218] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  35. O.A. Castro-Alvaredo, A. Fring, C. Korff and J.L. Miramontes, Thermodynamic Bethe ansatz of the homogeneous sine-Gordon models, Nucl. Phys. B 575 (2000) 535 [hep-th/9912196] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  36. O.A. Castro Alvaredo and J.L. Miramontes, Massive symmetric space sine-Gordon soliton theories and perturbed conformal field theory, Nucl. Phys. B 581 (2000) 643 [hep-th/0002219] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  37. O.A. Castro-Alvaredo, Bootstrap methods in 1 + 1 dimensional quantum field theories: The homogeneous sine-Gordon models, hep-th/0109212 [SPIRES].

  38. J.L. Miramontes, T-duality in massive integrable field theories: The homogeneous and complex sine-Gordon models, Nucl. Phys. B 702 (2004) 419 [hep-th/0408119] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. J.L. Miramontes, Searching for new homogeneous sine-Gordon theories using T-duality symmetries, J. Phys. A 41 (2008) 304032 [arXiv:0711.2826] [SPIRES].

    MathSciNet  Google Scholar 

  40. H.J. de Vega and J.M. Maillet, Renormalization Character And Quantum S Matrix For A Classically Integrable Theory, Phys. Lett. B 101 (1981) 302 [SPIRES].

    ADS  Google Scholar 

  41. H.J. de Vega and J.M. Maillet, Semiclassical Quantization Of The Complex Sine-Gordon Field Theory, Phys. Rev. D 28 (1983) 1441 [SPIRES].

    ADS  Google Scholar 

  42. J.M. Maillet, Quantum U(1) Invariant Theory From Integrable Classical Models, Phys. Rev. D 26 (1982) 2755 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  43. A.A. Tseytlin, Effective action of gauged WZW model and exact string solutions, Nucl. Phys. B 399 (1993) 601 [hep-th/9301015] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. A.A. Tseytlin, Conformal σ-models corresponding to gauged Wess-Zumino-Witten theories, Nucl. Phys. B 411 (1994) 509 [hep-th/9302083] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. A.A. Tseytlin, On field redefinitions and exact solutions in string theory, Phys. Lett. B 317 (1993) 559 [hep-th/9308042] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  46. B. de Wit, M.T. Grisaru and P. van Nieuwenhuizen, The WZNW model at two loops, Nucl. Phys. B 408 (1993) 299 [hep-th/9307027] [SPIRES].

    Article  ADS  Google Scholar 

  47. A.M. Polyakov, Gauge fields and strings, Contemporary Concepts in Physics. Vol. 3, Harwood Academic Publishers, Chur Switzerland (1987) [SPIRES].

    Google Scholar 

  48. A.S. Schwarz and A.A. Tseytlin, Dilaton shift under duality and torsion of elliptic complex, Nucl. Phys. B 399 (1993) 691 [hep-th/9210015] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  49. T.H. Buscher, Path Integral Derivation of Quantum Duality in Nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  50. A.A. Tseytlin, Duality and dilaton, Mod. Phys. Lett. A 6 (1991) 1721 [SPIRES].

    MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Theoretical Physics Group, Blackett Laboratory, Imperial College, London, SW7 2AZ, U.K.

    B. Hoare & A. A. Tseytlin

  2. Lebedev Institute, Moscow, Russia

    A. A. Tseytlin

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  1. B. Hoare
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  2. A. A. Tseytlin
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Correspondence to B. Hoare.

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ArXiv ePrint: 1008.4914

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Hoare, B., Tseytlin, A.A. On the perturbative S-matrix of generalized sine-Gordon models. J. High Energ. Phys. 2010, 111 (2010). https://doi.org/10.1007/JHEP11(2010)111

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