Skip to main content
SpringerLink
Log in

The structure of non-abelian kinks

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We consider a class of integrable quantum field theories in 1 + 1 dimensions whose classical equations have kink solutions with internal collective coordinates that transform under a non-abelian symmetry group. These generalised sine-Gordon theories have been shown to be related to the world-sheet theory of the string in the AdS/CFT correspondence. We provide a careful analysis of the boundary conditions at spatial infinity complicated by the fact that they are defined by actions with a WZ term. We go on to describe the local and non-local charges carried by the kinks and end by showing that their structure is perfectly consistent with the exact factorizable S-matrices that have been proposed to describe these theories.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  3. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. A.A. Tseytlin, Spinning strings and AdS/CFT duality, hep-th/0311139 [INSPIRE].

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. A. Mikhailov, A nonlocal Poisson bracket of the sine-Gordon model, J. Geom. Phys. 61 (2011) 85 [hep-th/0511069] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. B. Hoare and A. Tseytlin, Pohlmeyer reduction for superstrings in AdS space, J. Phys. A 46 (2013) 015401 [arXiv:1209.2892] [INSPIRE].

    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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. 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] [INSPIRE].

    Article  ADS  Google Scholar 

  10. A. Mikhailov, Bihamiltonian structure of the classical superstring in AdS 5 × S 5, Adv. Theor. Math. Phys. 14 (2010) 1585 [hep-th/0609108] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  11. D.M. Schmidtt, Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction, JHEP 11 (2011) 067 [arXiv:1106.4796] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. F. Delduc, M. Magro and B. Vicedo, Alleviating the non-ultralocality of coset σ-models through a generalized Faddeev-Reshetikhin procedure, JHEP 08 (2012) 019 [arXiv:1204.0766] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. F. Delduc, M. Magro and B. Vicedo, Alleviating the non-ultralocality of the AdS 5 × S 5 superstring, JHEP 10 (2012) 061 [arXiv:1206.6050] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. 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] [INSPIRE].

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  18. 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] [INSPIRE].

    MathSciNet  Google Scholar 

  19. B. Hoare and A. Tseytlin, On the perturbative S-matrix of generalized sine-Gordon models, JHEP 11 (2010) 111 [arXiv:1008.4914] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. Y. Iwashita, R. Roiban and A. Tseytlin, Two-loop corrections to partition function of Pohlmeyer-reduced theory for AdS 5 × S 5 superstring, Phys. Rev. D 84 (2011) 126017 [arXiv:1109.5361] [INSPIRE].

    ADS  Google Scholar 

  21. 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 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. C.R. Fernandez-Pousa, M.V. Gallas, T.J. Hollowood and J.L. Miramontes, Solitonic integrable perturbations of parafermionic theories, Nucl. Phys. B 499 (1997) 673 [hep-th/9701109] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  26. T.J. Hollowood and J.L. Miramontes, The relativistic avatars of giant magnons and their S-matrix, JHEP 10 (2010) 012 [arXiv:1006.3667] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. B. Hoare, T.J. Hollowood and J.L. Miramontes, A relativistic relative of the magnon S-matrix, JHEP 11 (2011) 048 [arXiv:1107.0628] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. B. Hoare, T.J. Hollowood and J.L. Miramontes, Restoring Unitarity in the q-Deformed World-Sheet S-matrix, arXiv:1303.1447 [INSPIRE].

  29. T.J. Hollowood and J.L. Miramontes, Classical and quantum solitons in the symmetric space sine-Gordon theories, JHEP 04 (2011) 119 [arXiv:1012.0716] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. T.J. Hollowood and J.L. Miramontes, The AdS 5 × S 5 semi-symmetric space sine-Gordon theory, JHEP 05 (2011) 136 [arXiv:1104.2429] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. T.J. Hollowood, J.L. Miramontes and D.M. Schmidtt, The semi-classical quantum group, to appear.

  32. E. Witten, Nonabelian bosonization in two-dimensions, Commun. Math. Phys. 92 (1984) 455 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. A.Y. Alekseev and V. Schomerus, D-branes in the WZW model, Phys. Rev. D 60 (1999) 061901 [hep-th/9812193] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  34. K. Gawedzki, Conformal field theory: a case study, hep-th/9904145 [INSPIRE].

  35. K. Gawedzki, Boundary WZW, G/H, G/G and CS theories, Annales Henri Poincaré 3 (2002) 847 [hep-th/0108044] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. S. Elitzur and G. Sarkissian, D branes on a gauged WZW model, Nucl. Phys. B 625 (2002) 166 [hep-th/0108142] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. T. Kubota, J. Rasmussen, M.A. Walton and J.-G. Zhou, Maximally symmetric D-branes in gauged WZW models, Phys. Lett. B 544 (2002) 192 [hep-th/0112078] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. T.J. Hollowood and J.L. Miramontes, The semi-classical spectrum of solitons and giant magnons, JHEP 05 (2011) 062 [arXiv:1103.3148] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. D. Bernard and A. Leclair, Quantum group symmetries and nonlocal currents in 2 − D QFT, Commun. Math. Phys. 142 (1991) 99 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. M.F. De Groot, T.J. Hollowood and J.L. Miramontes, Generalized Drinfeld-Sokolov hierarchies, Commun. Math. Phys. 145 (1992) 57 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  41. G. Felder, K. Gawedzki and A. Kupiainen, Spectra of Wess-Zumino-Witten models with arbitrary simple groups, Commun. Math. Phys. 117 (1988) 127 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. J.M. Figueroa-O’Farrill and N. Mohammedi, Gauging the Wess-Zumino term of a σ-model with boundary, JHEP 08 (2005) 086 [hep-th/0506049] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. B. Julia and S. Silva, Currents and superpotentials in classical gauge invariant theories. 1. Local results with applications to perfect fluids and general relativity, Class. Quant. Grav. 15 (1998) 2173 [gr-qc/9804029] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. E. Dyer and K. Hinterbichler, Boundary terms, variational principles and higher derivative modified gravity, Phys. Rev. D 79 (2009) 024028 [arXiv:0809.4033] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  45. L. Abbott and S. Deser, Charge Definition in Nonabelian Gauge Theories, Phys. Lett. B 116 (1982) 259 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. S. Silva, On superpotentials and charge algebras of gauge theories, Nucl. Phys. B 558 (1999) 391 [hep-th/9809109] [INSPIRE].

    Article  ADS  Google Scholar 

  47. J.M. Maldacena, G.W. Moore and N. Seiberg, Geometrical interpretation of D-branes in gauged WZW models, JHEP 07 (2001) 046 [hep-th/0105038] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. L. Jeffrey and J. Weitsman, Bohr-Sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula, Commun. Math. Phys. 150 (1992) 593 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. L.C. Jeffrey and A.-L. Mare, Products of conjugacy classes in SU(2), Canad. Math. Bull. 48 (2005) 90 [math/0211424].

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Swansea University, Swansea, SA2 8PP, U.K.

    Timothy J. Hollowood

  2. Departamento de Física de Partículas and IGFAE, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    J. Luis Miramontes

  3. Instituto de Física Teórica IFT/UNESP, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, CEP 01140-070, São Paulo, SP, Brasil

    David M. Schmidtt

Authors
  1. Timothy J. Hollowood
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Luis Miramontes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David M. Schmidtt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Luis Miramontes.

Additional information

ArXiv ePrint: 1306.6651

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hollowood, T.J., Miramontes, J.L. & Schmidtt, D.M. The structure of non-abelian kinks. J. High Energ. Phys. 2013, 58 (2013). https://doi.org/10.1007/JHEP10(2013)058

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP10(2013)058

Keywords

Search

Navigation