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Inequivalent light-cone gauge-fixings of strings on $AdS_n \times S^n$ backgrounds

Published 28 Dec 2023 in hep-th | (2312.17056v2)

Abstract: Light-cone gauge-fixed sigma-models on $AdS_n\times Sn$ backgrounds play an important role in the integrability formulation of the AdS/CFT correspondence. The string spectrum of the sigma-model is gauge-independent, however the Hamiltonian and scattering matrix of the transverse worldsheet fields are not. We study how these change for a large family of inequivalent light-cone gauges, which are interpreted as $T\bar{T}$, $\tilde{J}T_\tau$, $JT_\sigma$ and $J\tau$ deformations. We investigate the moduli space of equivalent light-cone gauges and, specialising to $AdS_5 \times S5$, compute the different light-cone gauge symmetry algebras, well-known to be $\mathfrak{psu}(2|2){\oplus 2} \oplus \mathfrak{u}(1){\oplus 2}$ for the standard gauge-fixing. Many integrable deformations require a non-standard light-cone gauge, hence our classification and analysis of inequivalent gauges will be important for analysing such models.

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References (51)
  1. J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity”, Adv. Theor. Math. Phys. 2, 231 (1998), hep-th/9711200.
  2. M. Kruczenski, A. V. Ryzhov and A. A. Tseytlin, “Large spin limit 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 string theory and low-energy expansion of ferromagnetic spin chains”, Nucl. Phys. B 692, 3 (2004), hep-th/0403120.
  3. M. Kruczenski and A. A. Tseytlin, “Semiclassical relativistic strings in S5superscript𝑆5S^{5}italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT and long coherent operators in N=4 SYM theory”, JHEP 0409, 038 (2004), hep-th/0406189.
  4. G. Arutyunov and S. Frolov, “Integrable Hamiltonian for classical strings on 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 0502, 059 (2005), hep-th/0411089.
  5. G. Arutyunov and S. Frolov, “Uniform light-cone gauge for strings in 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: Solving SU(1|1) sector”, JHEP 0601, 055 (2006), hep-th/0510208.
  6. G. Arutyunov and S. Frolov, “Foundations of the 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. Part I”, J. Phys. A 42, 254003 (2009), arxiv:0901.4937.
  7. I. Bena, J. Polchinski and R. Roiban, “Hidden symmetries of the 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”, Phys. Rev. D 69, 046002 (2004), hep-th/0305116.
  8. A. Babichenko, B. Stefanski, Jr. and K. Zarembo, “Integrability and the AdS(3)/CFT(2) correspondence”, JHEP 1003, 058 (2010), arxiv:0912.1723.
  9. G. Arutyunov, S. Frolov, J. Plefka and M. Zamaklar, “The Off-shell Symmetry Algebra of the Light-cone 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”, J. Phys. A 40, 3583 (2007), hep-th/0609157.
  10. R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefanski, “The complete A⁢d⁢S3×S3×T4𝐴𝑑subscript𝑆3superscript𝑆3superscript𝑇4AdS_{3}\times S^{3}\times T^{4}italic_A italic_d italic_S start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT × italic_T start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT worldsheet S matrix”, JHEP 1410, 066 (2014), arxiv:1406.0453.
  11. T. Lloyd, O. Ohlsson Sax, A. Sfondrini and B. Stefański, Jr., “The complete worldsheet S matrix of superstrings on A⁢d⁢S3×S3×T4𝐴𝑑subscript𝑆3superscript𝑆3superscript𝑇4AdS_{3}\times S^{3}\times T^{4}italic_A italic_d italic_S start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT × italic_T start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT with mixed three-form flux”, Nucl. Phys. B 891, 570 (2015), arxiv:1410.0866.
  12. M. Baggio and A. Sfondrini, “Strings on NS-NS Backgrounds as Integrable Deformations”, Phys. Rev. D 98, 021902 (2018), arxiv:1804.01998.
  13. 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.
  14. S. Frolov, “T⁢T¯𝑇normal-¯𝑇T{\overline{T}}italic_T over¯ start_ARG italic_T end_ARG, J~⁢Jnormal-~𝐽𝐽\widetilde{J}Jover~ start_ARG italic_J end_ARG italic_J, J⁢T𝐽𝑇JTitalic_J italic_T and J~⁢Tnormal-~𝐽𝑇\widetilde{J}Tover~ start_ARG italic_J end_ARG italic_T deformations”, J. Phys. A 53, 025401 (2020), arxiv:1907.12117.
  15. B. Hoare, “Integrable deformations of sigma models”, J. Phys. A 55, 093001 (2022), arxiv:2109.14284.
  16. C. Klimcik, “Yang-Baxter sigma models and dS/AdS T duality”, JHEP 0212, 051 (2002), hep-th/0210095.
  17. F. Delduc, M. Magro and B. Vicedo, “An integrable deformation of the 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 action”, Phys. Rev. Lett. 112, 051601 (2014), arxiv:1309.5850.
  18. I. Kawaguchi, T. Matsumoto and K. Yoshida, “Jordanian deformations of the 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”, JHEP 1404, 153 (2014), arxiv:1401.4855.
  19. S. J. van Tongeren, “On classical Yang-Baxter based deformations of the 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”, JHEP 1506, 048 (2015), arxiv:1504.05516.
  20. I. V. Cherednik, “Relativistically Invariant Quasiclassical Limits of Integrable Two-dimensional Quantum Models”, Theor. Math. Phys. 47, 422 (1981).
  21. S. Lacroix and A. Wallberg, “An elliptic integrable deformation of the Principal Chiral Model”, arxiv:2311.09301.
  22. B. Hoare, A. L. Retore and F. K. Seibold, “Elliptic deformations of the A⁢d⁢S3×S3×T4𝐴𝑑subscript𝑆3superscript𝑆3superscript𝑇4{AdS}_{3}\times{S}^{3}\times{T}^{4}italic_A italic_d italic_S start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT × italic_T start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT string”, arxiv:2312.14031.
  23. G. Arutyunov, S. Frolov and M. Zamaklar, “Finite-size Effects from Giant Magnons”, Nucl. Phys. B 778, 1 (2007), hep-th/0606126.
  24. S. Giombi, R. Ricci, R. Roiban, A. A. Tseytlin and C. Vergu, “Quantum 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 in the AdS light-cone gauge”, JHEP 1003, 003 (2010), arxiv:0912.5105.
  25. G. Arutyunov and S. J. van Tongeren, “Double Wick rotating Green-Schwarz strings”, JHEP 1505, 027 (2015), arxiv:1412.5137.
  26. K. Zarembo, “Worldsheet spectrum in AdS(4)/CFT(3) correspondence”, JHEP 0904, 135 (2009), arxiv:0903.1747.
  27. J. L. Miramontes, “Pohlmeyer reduction revisited”, JHEP 0810, 087 (2008), arxiv:0808.3365.
  28. R. Borsato and S. Driezen, “All Jordanian deformations of the 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”, SciPost Phys. 14, 160 (2023), arxiv:2212.11269.
  29. J. A. Minahan, “Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills”, Lett. Math. Phys. 99, 33 (2012), arxiv:1012.3983.
  30. S. Dubovsky, V. Gorbenko and M. Mirbabayi, “Asymptotic fragility, near AdS22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT holography and T⁢T¯𝑇normal-¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG”, JHEP 1709, 136 (2017), arxiv:1706.06604.
  31. T. Anous and M. Guica, “A general definition of J⁢Ta𝐽subscript𝑇𝑎JT_{a}italic_J italic_T start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT-deformed QFTs”, SciPost Phys. 10, 096 (2021), arxiv:1911.02031.
  32. S. Dubovsky, S. Negro and M. Porrati, “Topological gauging and double current deformations”, JHEP 2305, 240 (2023), arxiv:2302.01654.
  33. S. F. Hassan and A. Sen, “Marginal deformations of WZNW and coset models from O(d,d) transformation”, Nucl. Phys. B 405, 143 (1993), hep-th/9210121.
  34. M. Henningson and C. R. Nappi, “Duality, marginal perturbations and gauging”, Phys. Rev. D 48, 861 (1993), hep-th/9301005.
  35. R. Borsato, “Lecture notes on current-current deformations”, arxiv:2312.13847.
  36. 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?”, SciPost Phys. Core 5, 028 (2022), arxiv:2112.10279.
  37. B. Doyon, J. Durnin and T. Yoshimura, “The Space of Integrable Systems from Generalised T⁢T¯𝑇normal-¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG-Deformations”, SciPost Phys. 13, 072 (2022), arxiv:2105.03326.
  38. V. G. Drinfeld, “Constant quasiclassical solutions of the Yang–Baxter quantum equation”, in: “Doklady Akademii Nauk”, pp. 531–535.
  39. N. Reshetikhin, “Multiparameter quantum groups and twisted quasitriangular Hopf algebras”, Lett. Math. Phys. 20, 331 (1990).
  40. A. Giaquinto and J. J. Zhang, “Bialgebra actions, twists, and universal deformation formulas”, J. Pure Appl. Algebra 128, 133 (1998), hep-th/9411140.
  41. F. Levkovich-Maslyuk, “The Bethe ansatz”, J. Phys. A 49, 323004 (2016), arxiv:1606.02950.
  42. A. L. Retore, “Introduction to classical and quantum integrability”, J. Phys. A 55, 173001 (2022), arxiv:2109.14280.
  43. S. Demulder, S. Driezen, B. Knighton, G. Oling, A. L. Retore, F. K. Seibold, A. Sfondrini and Z. Yan, “Exact approaches on the string worldsheet”, arxiv:2312.12930.
  44. N. Beisert, “The SU(2|2) dynamic S-matrix”, Adv. Theor. Math. Phys. 12, 945 (2008), hep-th/0511082.
  45. G. Arutyunov and S. Frolov, “On 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 String S-matrix”, Phys. Lett. B 639, 378 (2006), hep-th/0604043.
  46. J. A. Minahan and K. Zarembo, “The Bethe ansatz for N=4 superYang-Mills”, JHEP 0303, 013 (2003), hep-th/0212208.
  47. N. Beisert, “The complete one loop dilatation operator of N=4 superYang-Mills theory”, Nucl. Phys. B 676, 3 (2004), hep-th/0307015.
  48. S. J. van Tongeren, “Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory”, Nucl. Phys. B 904, 148 (2016), arxiv:1506.01023.
  49. S. J. van Tongeren, “Almost abelian twists and AdS/CFT”, Phys. Lett. B 765, 344 (2017), arxiv:1610.05677.
  50. T. Meier and S. J. van Tongeren, “Quadratic Twist-Noncommutative Gauge Theory”, Phys. Rev. Lett. 131, 121603 (2023), arxiv:2301.08757.
  51. T. Meier and S. J. van Tongeren, “Gauge theory on twist-noncommutative spaces”, JHEP 2312, 045 (2023), arxiv:2305.15470.
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