Papers
Topics
Authors
Recent
Search
2000 character limit reached

On exactly solvable Yang-Baxter models and enhanced symmetries

Published 12 Mar 2024 in hep-th | (2403.07365v3)

Abstract: We study Yang-Baxter deformations of the flat space string that result in exactly solvable models, finding the Nappi-Witten model and its higher dimensional generalizations. We then consider the spectra of these models obtained by canonical quantization in light-cone gauge, and match them with an integrability-based Bethe ansatz approach. By considering a generalized light-cone gauge we can describe the model by a nontrivially Drinfel'd twisted S matrix, explicitly verifying the twisted structure expected for such deformations. Next, the reformulation of the Nappi-Witten model as a Yang-Baxter deformation shows that Yang-Baxter models can have more symmetries than suggested by the $r$ matrix defining the deformation. We discuss these enhanced symmetries in more detail for some trivial and nontrivial examples. Finally, we observe that there are nonunimodular but Weyl-invariant Yang-Baxter models of a type not previously considered.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (53)
  1. R. Metsaev and A. A. Tseytlin, “Type IIB superstring action in AdS(5) x S**5 background”, Nucl.Phys. B533, 109 (1998), hep-th/9805028.
  2. G. Arutyunov and S. Frolov, “Foundations of the AdS5×S5subscriptnormal-AdS5superscriptnormal-S5{\rm AdS}_{5}\times{\rm S}^{5}roman_AdS start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × roman_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT Superstring. Part I”, J.Phys. A42, 254003 (2009), arxiv:0901.4937.
  3. I. Bena, J. Polchinski and R. Roiban, “Hidden symmetries of the 𝐴𝑑𝑆5×S5subscript𝐴𝑑𝑆5superscript𝑆5\mathit{AdS}_{5}\times\mathit{S}^{5}italic_AdS start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstring”, Phys. Rev. D69, 046002 (2004), hep-th/0305116.
  4. N. Beisert, C. Ahn, L. F. Alday, Z. Bajnok, J. M. Drummond et al., “Review of AdS/CFT Integrability: An Overview”, Lett.Math.Phys. 99, 3 (2012), arxiv:1012.3982.
  5. D. Bombardelli, A. Cagnazzo, R. Frassek, F. Levkovich-Maslyuk, F. Loebbert, S. Negro, I. M. Szécsényi, A. Sfondrini, S. J. van Tongeren and A. Torrielli, “An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction”, J.Phys.A 49, 320301 (2016), arxiv:1606.02945.
  6. B. Basso and A. G. Tumanov, “Wilson loop duality and OPE for super form factors of half-BPS operators”, JHEP 2402, 022 (2024), arxiv:2308.08432.
  7. B. Eden, M. Gottwald, D. le Plat and T. Scherdin, “Anomalous dimensions from the 𝒩=4𝒩4\mathcal{N}=4caligraphic_N = 4 SYM hexagon”, arxiv:2310.04392.
  8. C. Klimcik, “Yang-Baxter sigma models and dS/AdS T duality”, JHEP 0212, 051 (2002), hep-th/0210095.
  9. C. Klimcik, “On integrability of the Yang-Baxter sigma-model”, J.Math.Phys. 50, 043508 (2009), arxiv:0802.3518.
  10. F. Delduc, M. Magro and B. Vicedo, “An integrable deformation of the AdS5×S5subscriptnormal-AdS5superscriptnormal-S5{\rm AdS}_{5}\times{\rm S}^{5}roman_AdS start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × roman_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstring action”, Phys.Rev.Lett. 112, 051601 (2014), arxiv:1309.5850.
  11. I. Kawaguchi, T. Matsumoto and K. Yoshida, “Jordanian deformations of the AdS5×S5subscriptnormal-AdS5superscriptnormal-S5{\rm AdS}_{5}\times{\rm S}^{5}roman_AdS start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × roman_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstring”, JHEP 1404, 153 (2014), arxiv:1401.4855.
  12. F. Delduc, M. Magro and B. Vicedo, “Derivation of the action and symmetries of the q𝑞qitalic_q-deformed AdS5×S5subscriptnormal-AdS5superscriptnormal-S5{\rm AdS}_{5}\times{\rm S}^{5}roman_AdS start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × roman_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstring”, JHEP 1410, 132 (2014), arxiv:1406.6286.
  13. S. J. van Tongeren, “On classical Yang-Baxter based deformations of the AdS×5{}_{5}\timesstart_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT ×S55{}^{5}start_FLOATSUPERSCRIPT 5 end_FLOATSUPERSCRIPT superstring”, JHEP 1506, 048 (2015), arxiv:1504.05516.
  14. B. Hoare, “Integrable Deformations of Sigma Models”, arxiv:2109.14284.
  15. 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. B903, 262 (2016), arxiv:1511.05795.
  16. L. Wulff and A. A. Tseytlin, “Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations”, JHEP 1606, 174 (2016), arxiv:1605.04884.
  17. L. Wulff, “Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly”, Phys. Lett. B 781, 417 (2018), arxiv:1803.07391.
  18. R. Borsato and L. Wulff, “Target space supergeometry of η𝜂\etaitalic_η and λ𝜆\lambdaitalic_λ-deformed strings”, JHEP 1610, 045 (2016), arxiv:1608.03570.
  19. G. Arutyunov, R. Borsato and S. Frolov, “S-matrix for strings on 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”, JHEP 1404, 002 (2014), arxiv:1312.3542.
  20. G. Arutyunov, M. de Leeuw and S. J. van Tongeren, “The exact spectrum and mirror duality of the (𝐴𝑑𝑆5×S5)ηsubscriptsubscript𝐴𝑑𝑆5superscript𝑆5𝜂(\text{AdS}_{5}{\times}S^{5})_{\eta}( AdS start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT ) start_POSTSUBSCRIPT italic_η end_POSTSUBSCRIPT superstring”, Theor. Math. Phys. 182, 23 (2015), arxiv:1403.6104, [Teor. Mat. Fiz.182,no.1,28(2014)].
  21. R. Klabbers and S. J. van Tongeren, “Quantum Spectral Curve for the eta-deformed AdS55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPTxS55{}^{5}start_FLOATSUPERSCRIPT 5 end_FLOATSUPERSCRIPT superstring”, Nucl. Phys. B925, 252 (2017), arxiv:1708.02894.
  22. F. K. Seibold, S. J. van Tongeren and Y. Zimmermann, “The twisted story of worldsheet scattering in 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”, JHEP 2012, 043 (2020), arxiv:2007.09136.
  23. F. K. Seibold and A. Sfondrini, “Bethe ansatz for quantum-deformed strings”, JHEP 2112, 015 (2021), arxiv:2109.08510.
  24. B. Vicedo, “Deformed integrable σ𝜎\sigmaitalic_σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles”, J. Phys. A48, 355203 (2015), arxiv:1504.06303.
  25. S. J. van Tongeren, “Yang–Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory”, Nucl. Phys. B904, 148 (2016), arxiv:1506.01023.
  26. S. J. van Tongeren, “Almost abelian twists and AdS/CFT”, Phys. Lett. B765, 344 (2017), arxiv:1610.05677.
  27. S. J. van Tongeren and Y. Zimmermann, “Do Drinfeld twists of 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 survive light-cone quantization?”, arxiv:2112.10279.
  28. R. Borsato, S. Driezen and J. L. Miramontes, “Homogeneous Yang-Baxter deformations as undeformed yet twisted models”, JHEP 2204, 053 (2022), arxiv:2112.12025.
  29. R. Borsato, S. Driezen, J. M. Nieto García and L. Wyss, “Semiclassical spectrum of a Jordanian deformation of AdS5×S5”, Phys. Rev. D 106, 066015 (2022), arxiv:2207.14748.
  30. R. Borsato, S. Driezen, B. Hoare, A. L. Retore and F. K. Seibold, “Inequivalent light-cone gauge-fixings of strings on A⁢d⁢Sn×Sn𝐴𝑑subscript𝑆𝑛superscript𝑆𝑛AdS_{n}\times S^{n}italic_A italic_d italic_S start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT backgrounds”, arxiv:2312.17056.
  31. K. Idiab and S. J. van Tongeren, “Yang-Baxter deformations of the flat space string”, Phys. Lett. B 835, 137499 (2022), arxiv:2205.13050.
  32. F. Delduc, M. Magro and B. Vicedo, “On classical q𝑞qitalic_q-deformations of integrable sigma-models”, JHEP 1311, 192 (2013), arxiv:1308.3581.
  33. S. Zakrzewski, “Poisson Structures on the Poincaré Group”, Communications in Mathematical Physics 185, 285 (1997), q-alg/9602001, http://dx.doi.org/10.1007/s002200050091.
  34. C. R. Nappi and E. Witten, “A WZW model based on a nonsemisimple group”, Phys. Rev. Lett. 71, 3751 (1993), hep-th/9310112.
  35. P. Forgacs, P. A. Horvathy, Z. Horvath and L. Palla, “The Nappi-Witten string in the light cone gauge”, Acta Phys. Hung. A 1, 65 (1995), hep-th/9503222.
  36. A. Dei and A. Sfondrini, “Integrable S matrix, mirror TBA and spectrum for the stringy AdS33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT × S33{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPT × S33{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPT × S11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT WZW model”, JHEP 1902, 072 (2019), arxiv:1812.08195.
  37. G. Arutyunov, S. Frolov and M. Zamaklar, “The Zamolodchikov-Faddeev algebra for AdS5×S5subscriptnormal-AdS5superscriptnormal-S5{\rm AdS}_{5}\times{\rm S}^{5}roman_AdS start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × roman_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstring”, JHEP 0704, 002 (2007), hep-th/0612229.
  38. S. Frolov, “T⁢T¯𝑇normal-¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG Deformation and the Light-Cone Gauge”, Proc. Steklov Inst. Math. 309, 107 (2020), arxiv:1905.07946.
  39. F. A. Smirnov and A. B. Zamolodchikov, “On space of integrable quantum field theories”, Nucl. Phys. B 915, 363 (2017), arxiv:1608.05499.
  40. A. Cavaglià, S. Negro, I. M. Szécsényi and R. Tateo, “T⁢T¯𝑇normal-¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG-deformed 2D Quantum Field Theories”, JHEP 1610, 112 (2016), arxiv:1608.05534.
  41. M. Baggio and A. Sfondrini, “Strings on NS-NS Backgrounds as Integrable Deformations”, Phys. Rev. D 98, 021902 (2018), arxiv:1804.01998.
  42. S. Dubovsky, R. Flauger and V. Gorbenko, “Solving the Simplest Theory of Quantum Gravity”, JHEP 1209, 133 (2012), arxiv:1205.6805.
  43. A. Sfondrini and S. J. van Tongeren, “T⁢T¯𝑇normal-¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG deformations as T⁢s⁢T𝑇𝑠𝑇TsTitalic_T italic_s italic_T transformations”, Phys. Rev. D 101, 066022 (2020), arxiv:1908.09299.
  44. H. Kyono and K. Yoshida, “Yang–Baxter invariance of the Nappi–Witten model”, Nucl. Phys. B 905, 242 (2016), arxiv:1511.00404.
  45. Y. Sakatani, “Poisson–Lie T-plurality for WZW backgrounds”, PTEP 2021, 103B03 (2021), arxiv:2102.01069.
  46. J. Figueroa-O’Farrill, “Lie algebraic Carroll/Galilei duality”, J. Math. Phys. 64, 013503 (2023), arxiv:2210.13924.
  47. S. Stanciu and J. M. Figueroa-O’Farrill, “Penrose limits of Lie branes and a Nappi-Witten brane world”, JHEP 0306, 025 (2003), hep-th/0303212.
  48. E. Kiritsis and C. Kounnas, “String propagation in gravitational wave backgrounds”, Phys. Lett. B 320, 264 (1994), hep-th/9310202, [Addendum: Phys.Lett.B 325, 536 (1994)].
  49. C. Klimcik and A. A. Tseytlin, “Duality invariant class of exact string backgrounds”, Phys. Lett. B 323, 305 (1994), hep-th/9311012.
  50. D. Osten and S. J. van Tongeren, “Abelian Yang–Baxter deformations and TsT transformations”, Nucl. Phys. B915, 184 (2017), arxiv:1608.08504.
  51. F. Delduc, B. Hoare, T. Kameyama, S. Lacroix and M. Magro, “Three-parameter integrable deformation of ℤ4subscriptℤ4\mathbb{Z}_{4}blackboard_Z start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT permutation supercosets”, JHEP 1901, 109 (2019), arxiv:1811.00453.
  52. S. Hronek and L. Wulff, “Relaxing unimodularity for Yang-Baxter deformed strings”, JHEP 2010, 065 (2020), arxiv:2007.15663.
  53. R. Borsato and L. Wulff, “Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings”, JHEP 1808, 027 (2018), arxiv:1806.04083.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

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

Generate Now

Collections

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

Sign Up

Tweets

Sign up for free to view the 3 tweets with 1 like about this paper.

Sign Up for Free