Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 43 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 21 tok/s Pro
GPT-5 High 20 tok/s Pro
GPT-4o 95 tok/s Pro
Kimi K2 180 tok/s Pro
GPT OSS 120B 443 tok/s Pro
Claude Sonnet 4.5 32 tok/s Pro
2000 character limit reached

On quantum Poisson-Lie T-duality of WZNW models (2311.18530v3)

Published 30 Nov 2023 in hep-th

Abstract: We study Poisson-Lie T-duality of the Wess-Zumino-Novikov-Witten (WZNW) models which are obtained from a class of Drinfel'd doubles and its generalization. In this case, the resultant WZNW models are known to be classically self-dual under Poisson-Lie T-duality. We describe an explicit construction of the associated currents, and discuss the conformal invariance under this duality. In a concrete example of the SU(2) WZNW model, we find that the self-duality is represented as a chiral automorphism of the $\widehat{\mathfrak{su}}(2)$ affine Lie algebra, though the transformation of the currents is non-local and non-linear. This classical automorphism can be promoted to the quantum one through the parafermionic formulation of $\widehat{\mathfrak{su}}(2)$, which in turn induces an isomorphism of the WZNW model. We thus find a full quantum equivalence of the dual pair under Poisson-Lie T-duality. The isomorphism is represented by a sign-change of a chiral boson or the order-disorder duality of the parafermionic conformal field theory as in Abelian T-duality on tori or in the mirror symmetry of the Gepner model.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (78)
  1. K. Kikkawa and M. Yamasaki, “Casimir Effects in Superstring Theories,” Phys. Lett. B 149 (1984), 357-360.
  2. N. Sakai and I. Senda, “Vacuum Energies of String Compactified on Torus,” Prog. Theor. Phys. 75 (1986), 692 [erratum: Prog. Theor. Phys. 77 (1987), 773].
  3. T. H. Buscher, “A Symmetry of the String Background Field Equations,” Phys. Lett. B 194 (1987), 59-62.
  4. M. J. Duff, “Duality Rotations in String Theory,” Nucl. Phys. B 335 (1990), 610.
  5. A. Giveon and M. Rocek, “Generalized duality in curved string backgrounds,” Nucl. Phys. B 380 (1992), 128-146 [arXiv:hep-th/9112070 [hep-th]].
  6. M. Rocek and E. P. Verlinde, “Duality, quotients, and currents,” Nucl. Phys. B 373 (1992), 630-646 [arXiv:hep-th/9110053 [hep-th]].
  7. E. Alvarez, L. Alvarez-Gaume, J. L. F. Barbon and Y. Lozano, “Some global aspects of duality in string theory,” Nucl. Phys. B 415 (1994), 71-100 [arXiv:hep-th/9309039 [hep-th]].
  8. E. Alvarez, L. Alvarez-Gaume and Y. Lozano, “A Canonical approach to duality transformations,” Phys. Lett. B 336 (1994), 183-189 [arXiv:hep-th/9406206 [hep-th]].
  9. X. C. de la Ossa and F. Quevedo, “Duality symmetries from nonAbelian isometries in string theory,” Nucl. Phys. B 403 (1993), 377-394 [arXiv:hep-th/9210021 [hep-th]].
  10. A. Giveon and M. Rocek, “On nonAbelian duality,” Nucl. Phys. B 421 (1994), 173-190 [arXiv:hep-th/9308154 [hep-th]].
  11. E. Alvarez, L. Alvarez-Gaume and Y. Lozano, “On nonAbelian duality,” Nucl. Phys. B 424 (1994), 155-183 [arXiv:hep-th/9403155 [hep-th]].
  12. C. Klimcik and P. Severa, “Dual nonAbelian duality and the Drinfeld double,” Phys. Lett. B 351 (1995), 455-462 [arXiv:hep-th/9502122 [hep-th]].
  13. C. Klimcik, “Poisson-Lie T duality,” Nucl. Phys. B Proc. Suppl. 46 (1996), 116-121 [arXiv:hep-th/9509095 [hep-th]].
  14. C. Klimcik and P. Severa, “Poisson-Lie T duality and loop groups of Drinfeld doubles,” Phys. Lett. B 372 (1996), 65-71 [arXiv:hep-th/9512040 [hep-th]].
  15. K. Sfetsos, “Canonical equivalence of nonisometric sigma models and Poisson-Lie T duality,” Nucl. Phys. B 517 (1998), 549-566 [arXiv:hep-th/9710163 [hep-th]].
  16. A. Bossard and N. Mohammedi, “Poisson-Lie duality in the string effective action,” Nucl. Phys. B 619 (2001), 128-154 [arXiv:hep-th/0106211 [hep-th]].
  17. W. Siegel, “Superspace duality in low-energy superstrings,” Phys. Rev. D 48 (1993), 2826-2837 [arXiv:hep-th/9305073 [hep-th]].
  18. C. Hull and B. Zwiebach, “Double Field Theory,” JHEP 09 (2009), 099 [arXiv:0904.4664 [hep-th]].
  19. O. Hohm, C. Hull and B. Zwiebach, “Generalized metric formulation of double field theory,” JHEP 08 (2010), 008 [arXiv:1006.4823 [hep-th]].
  20. D. Geissbuhler, D. Marques, C. Nunez and V. Penas, “Exploring Double Field Theory,” JHEP 06 (2013), 101 [arXiv:1304.1472 [hep-th]].
  21. F. Hassler, “Poisson-Lie T-duality in Double Field Theory,” Phys. Lett. B 807 (2020), 135455 [arXiv:1707.08624 [hep-th]].
  22. P. Ševera and F. Valach, “Courant Algebroids, Poisson–Lie T-Duality, and Type II Supergravities,” Commun. Math. Phys. 375 (2020) no.1, 307-344 [arXiv:1810.07763 [math.DG]].
  23. S. Demulder, F. Hassler and D. C. Thompson, “Doubled aspects of generalised dualities and integrable deformations,” JHEP 02 (2019), 189 [arXiv:1810.11446 [hep-th]].
  24. Y. Sakatani, “Type II DFT solutions from Poisson-Lie T-duality/plurality,” [arXiv:1903.12175 [hep-th]].
  25. G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A. A. Tseytlin, “Scale invariance of the η𝜂\etaitalic_η-deformed A⁢d⁢S5×S5𝐴𝑑subscript𝑆5superscript𝑆5AdS_{5}\times S^{5}italic_A italic_d italic_S start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstring, T-duality and modified type II equations,” Nucl. Phys. B 903 (2016), 262-303 [arXiv:1511.05795 [hep-th]].
  26. L. Wulff and A. A. Tseytlin, “Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations,” JHEP 06 (2016), 174 [arXiv:1605.04884 [hep-th]].
  27. M. Gasperini, R. Ricci and G. Veneziano, “A Problem with nonAbelian duality?,” Phys. Lett. B 319 (1993), 438-444 [arXiv:hep-th/9308112 [hep-th]].
  28. J. i. Sakamoto, Y. Sakatani and K. Yoshida, “Weyl invariance for generalized supergravity backgrounds from the doubled formalism,” PTEP 2017 (2017) no.5, 053B07 [arXiv:1703.09213 [hep-th]].
  29. L. Wulff, “Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly,” Phys. Lett. B 781 (2018), 417-422 [arXiv:1803.07391 [hep-th]].
  30. J. Balog, P. Forgacs, N. Mohammedi, L. Palla and J. Schnittger, “On quantum T duality in sigma models,” Nucl. Phys. B 535 (1998), 461-482 [arXiv:hep-th/9806068 [hep-th]].
  31. K. Sfetsos, “Duality invariant class of two-dimensional field theories,” Nucl. Phys. B 561 (1999), 316-340 [arXiv:hep-th/9904188 [hep-th]].
  32. K. Sfetsos and K. Siampos, “Quantum equivalence in Poisson-Lie T-duality,” JHEP 06 (2009), 082 [arXiv:0904.4248 [hep-th]].
  33. K. Sfetsos, K. Siampos and D. C. Thompson, “Renormalization of Lorentz non-invariant actions and manifest T-duality,” Nucl. Phys. B 827 (2010), 545-564 [arXiv:0910.1345 [hep-th]].
  34. F. Hassler and T. Rochais, “α′superscript𝛼′\alpha^{\prime}italic_α start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT-Corrected Poisson-Lie T-Duality,” Fortsch. Phys. 68 (2020) no.9, 2000063 [arXiv:2007.07897 [hep-th]].
  35. R. Borsato and L. Wulff, “Quantum Correction to Generalized T𝑇Titalic_T Dualities,” Phys. Rev. Lett. 125 (2020) no.20, 201603 [arXiv:2007.07902 [hep-th]].
  36. T. Codina and D. Marques, “Generalized Dualities and Higher Derivatives,” JHEP 10 (2020), 002 [arXiv:2007.09494 [hep-th]].
  37. A. Y. Alekseev, C. Klimcik and A. A. Tseytlin, “Quantum Poisson-Lie T duality and WZNW model,” Nucl. Phys. B 458 (1996), 430-444 [arXiv:hep-th/9509123 [hep-th]].
  38. E. Tyurin and R. von Unge, “Poisson-lie T duality: The Path integral derivation,” Phys. Lett. B 382 (1996), 233-240 [arXiv:hep-th/9512025 [hep-th]].
  39. R. Von Unge, “Poisson Lie T plurality,” JHEP 07 (2002), 014 [arXiv:hep-th/0205245 [hep-th]].
  40. C. Klimcik and P. Severa, “Open strings and D-branes in WZNW model,” Nucl. Phys. B 488 (1997), 653-676 [arXiv:hep-th/9609112 [hep-th]].
  41. V. A. Fateev and A. B. Zamolodchikov, “Parafermionic Currents in the Two-Dimensional Conformal Quantum Field Theory and Selfdual Critical Points in Z(n) Invariant Statistical Systems,” Sov. Phys. JETP 62 (1985), 215-225 LANDAU-1985-9.
  42. D. Gepner and Z. a. Qiu, “Modular Invariant Partition Functions for Parafermionic Field Theories,” Nucl. Phys. B 285 (1987), 423.
  43. B. R. Greene and M. R. Plesser, “Duality in Calabi-Yau Moduli Space,” Nucl. Phys. B 338 (1990), 15-37.
  44. B. R. Greene, “String theory on Calabi-Yau manifolds,” [arXiv:hep-th/9702155 [hep-th]].
  45. D. Gepner, “Space-Time Supersymmetry in Compactified String Theory and Superconformal Models,” Nucl. Phys. B 296 (1988), 757.
  46. M. R. Gaberdiel, “Abelian duality in WZW models,” Nucl. Phys. B 471 (1996), 217-232 [arXiv:hep-th/9601016 [hep-th]].
  47. J. M. Maldacena, G. W. Moore and N. Seiberg, “Geometrical interpretation of D-branes in gauged WZW models,” JHEP 07 (2001), 046 [arXiv:hep-th/0105038 [hep-th]].
  48. E. Kiritsis, “Exact duality symmetries in CFT and string theory,” Nucl. Phys. B 405 (1993), 109-142 [arXiv:hep-th/9302033 [hep-th]].
  49. A. Eghbali and A. Rezaei-Aghdam, “Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group H4subscript𝐻4H_{4}italic_H start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT,” Nucl. Phys. B 899 (2015), 165-179 [arXiv:1506.06233 [hep-th]].
  50. A. Eghbali, “Exact conformal field theories from mutually T-dualizable σ𝜎\sigmaitalic_σ-models,” Phys. Rev. D 99 (2019) no.2, 026001 [arXiv:1812.07664 [hep-th]].
  51. Y. Sakatani, “Poisson–Lie T-plurality for WZW backgrounds,” PTEP 2021 (2021) no.10, 103B03 [arXiv:2102.01069 [hep-th]].
  52. C. M. Hull and R. A. Reid-Edwards, “Non-geometric backgrounds, doubled geometry and generalised T-duality,” JHEP 09 (2009), 014 [arXiv:0902.4032 [hep-th]].
  53. R. A. Reid-Edwards, “Bi-Algebras, Generalised Geometry and T-Duality,” [arXiv:1001.2479 [hep-th]].
  54. C. M. Hull, “A Geometry for non-geometric string backgrounds,” JHEP 10 (2005), 065 [arXiv:hep-th/0406102 [hep-th]].
  55. R. Borsato, S. Driezen and F. Hassler, “An algebraic classification of solution generating techniques,” Phys. Lett. B 823 (2021), 136771 [arXiv:2109.06185 [hep-th]].
  56. C. Klimcik, “η𝜂\etaitalic_η and λ𝜆\lambdaitalic_λ deformations as E -models,” Nucl. Phys. B 900 (2015), 259-272 [arXiv:1508.05832 [hep-th]].
  57. L. Snobl and L. Hlavaty, “Classification of six-dimensional real Drinfeld doubles,” Int. J. Mod. Phys. A 17 (2002), 4043-4068 [arXiv:math/0202210 [math.QA]].
  58. R. Blumenhagen, P. du Bosque, F. Hassler and D. Lust, “Generalized Metric Formulation of Double Field Theory on Group Manifolds,” JHEP 08 (2015), 056 [arXiv:1502.02428 [hep-th]].
  59. S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer and G. Veneziano, “Remarks on nonAbelian duality,” Nucl. Phys. B 435 (1995), 147-171 [arXiv:hep-th/9409011 [hep-th]].
  60. J. J. Fernandez-Melgarejo, J. i. Sakamoto, Y. Sakatani and K. Yoshida, “T𝑇Titalic_T-folds from Yang-Baxter deformations,” JHEP 12 (2017), 108 [arXiv:1710.06849 [hep-th]].
  61. J. J. Fernández-Melgarejo, J. I. Sakamoto, Y. Sakatani and K. Yoshida, “Weyl invariance of string theories in generalized supergravity backgrounds,” Phys. Rev. Lett. 122 (2019) no.11, 111602 [arXiv:1811.10600 [hep-th]].
  62. J. I. Sakamoto and Y. Sakatani, “Local β𝛽\betaitalic_β-deformations and Yang-Baxter sigma model,” JHEP 06 (2018), 147 [arXiv:1803.05903 [hep-th]].
  63. G. Dibitetto, J. J. Fernandez-Melgarejo, D. Marques and D. Roest, “Duality orbits of non-geometric fluxes,” Fortsch. Phys. 60 (2012), 1123-1149 [arXiv:1203.6562 [hep-th]].
  64. V. G. Kac and D. H. Peterson, “On geometric invariant theory for infinite-dimensional groups,” in Lecture Notes in Math.1271 (1987)109. Wiley-Interscience, 1995.
  65. R. V. Moody and A. Pianzola, “Lie Algebras with Triangular Decompositions,” Wiley-Interscience, 1995.
  66. A. B. Zamolodchikov and V. A. Fateev, “Disorder Fields in Two-Dimensional Conformal Quantum Field Theory and N=2 Extended Supersymmetry,” Sov. Phys. JETP 63 (1986), 913-919.
  67. S. E. Parkhomenko, “On the quantum Poisson-Lie T duality and mirror symmetry,” J. Exp. Theor. Phys. 89 (1999), 5-12 [arXiv:hep-th/9812048 [hep-th]].
  68. S. K. Yang, “Marginal Deformation of Minimal N=2𝑁2N=2italic_N = 2 Superconformal Field Theories and the Witten Index,” Phys. Lett. B 209 (1988), 242-246.
  69. C. Klimcik and S. Parkhomenko, “Monodromic strings,” [arXiv:hep-th/0010084 [hep-th]].
  70. A. Giveon, M. Porrati and E. Rabinovici, “Target space duality in string theory,” Phys. Rept. 244 (1994), 77-202 [arXiv:hep-th/9401139 [hep-th]].
  71. D. Gepner, “New Conformal Field Theories Associated with Lie Algebras and their Partition Functions,” Nucl. Phys. B 290 (1987), 10-24.
  72. K. Lee and J. H. Park, “Covariant action for a string in ”doubled yet gauged” spacetime,” Nucl. Phys. B 880 (2014), 134-154 [arXiv:1307.8377 [hep-th]].
  73. K. Morand and J. H. Park, “Classification of non-Riemannian doubled-yet-gauged spacetime,” Eur. Phys. J. C 77 (2017) no.10, 685 [erratum: Eur. Phys. J. C 78 (2018) no.11, 901] [arXiv:1707.03713 [hep-th]].
  74. J. H. Park and S. Sugimoto, “String Theory and non-Riemannian Geometry,” Phys. Rev. Lett. 125 (2020) no.21, 211601 [arXiv:2008.03084 [hep-th]].
  75. Y. Satoh, Y. Sugawara and T. Wada, “Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant,” JHEP 02 (2016), 184 [arXiv:1512.05155 [hep-th]].
  76. Y. Satoh and Y. Sugawara, “Lie algebra lattices and strings on T-folds,” JHEP 02 (2017), 024 [arXiv:1611.08076 [hep-th]].
  77. Y. Satoh and Y. Sugawara, “Interactions of strings on a T-fold,” JHEP 06 (2022), 121 [arXiv:2203.05841 [hep-th]].
  78. S. Lacroix, “On a class of conformal ℰℰ\mathcal{E}caligraphic_E-models and their chiral Poisson algebras,” JHEP 06 (2023), 045 [arXiv:2304.04790 [hep-th]].
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up