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Integrability and non-integrability for holographic dual of Matrix model and non-Abelian T-dual of AdS$_5\times$S$^5$

Published 18 Oct 2023 in hep-th | (2310.11744v3)

Abstract: In this paper we study integrability and non-integrability for type-IIA supergravity background dual to deformed plane wave matrix model. From the bulk perspective, we estimate various chaos indicators that clearly shows chaotic string dynamics in the limit of small value of the parameter $L$ present in the theory. On the other hand, the string dynamics exhibits a non-chaotic motion for the large value of the parameter $L$ and therefore presumably an underlying integrable structure. Our findings reveals that the parameter $L$ in the type-IIA background acts as an interpolation between a non-integrable theory to an integrable theory in dual SCFTs.

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References (48)
  1. J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2, 231-252 (1998) doi:10.4310/ATMP.1998.v2.n2.a1 [arXiv:hep-th/9711200 [hep-th]].
  2. E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253-291 (1998) doi:10.4310/ATMP.1998.v2.n2.a2 [arXiv:hep-th/9802150 [hep-th]].
  3. K. Sfetsos, “Integrable interpolations: From exact CFTs to non-Abelian T-duals,” Nucl. Phys. B 880, 225-246 (2014) doi:10.1016/j.nuclphysb.2014.01.004 [arXiv:1312.4560 [hep-th]].
  4. T. J. Hollowood, J. L. Miramontes and D. M. Schmidtt, “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,” J. Phys. A 47, no.49, 495402 (2014) doi:10.1088/1751-8113/47/49/495402 [arXiv:1409.1538 [hep-th]].
  5. 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, no.5, 051601 (2014) doi:10.1103/PhysRevLett.112.051601 [arXiv:1309.5850 [hep-th]].
  6. J. Pal, H. Rathi, A. Lala and D. Roychowdhury, “Non-chaotic dynamics for Yang-Baxter deformed A⁢d⁢S4×C⁢P3𝐴𝑑subscript𝑆4𝐶superscript𝑃3AdS_{4}\times CP^{3}italic_A italic_d italic_S start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT × italic_C italic_P start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT superstrings,” [arXiv:2208.09599 [hep-th]].
  7. D. Roychowdhury, “Analytic integrability for holographic duals with J⁢T¯𝐽¯𝑇J\overline{T}italic_J over¯ start_ARG italic_T end_ARG deformations,” JHEP 09, 053 (2020) doi:10.1007/JHEP09(2020)053 [arXiv:2005.04457 [hep-th]].
  8. K. Filippas, C. Núñez and J. Van Gorsel, “Integrability and holographic aspects of six-dimensional 𝒩=(1, 0)𝒩1 0\mathcal{N}=\left(1,\ 0\right)caligraphic_N = ( 1 , 0 ) superconformal field theories,” JHEP 06, 069 (2019) doi:10.1007/JHEP06(2019)069 [arXiv:1901.08598 [hep-th]].
  9. L. A. Pando Zayas and C. A. Terrero-Escalante, “Chaos in the Gauge / Gravity Correspondence,” JHEP 09, 094 (2010) doi:10.1007/JHEP09(2010)094 [arXiv:1007.0277 [hep-th]].
  10. P. Basu, D. Das and A. Ghosh, “Integrability Lost,” Phys. Lett. B 699, 388-393 (2011) doi:10.1016/j.physletb.2011.04.027 [arXiv:1103.4101 [hep-th]].
  11. P. Basu and L. A. Pando Zayas, “Chaos rules out integrability of strings on AdS×5T1,1{}_{5}\times T^{1,1}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT × italic_T start_POSTSUPERSCRIPT 1 , 1 end_POSTSUPERSCRIPT,” Phys. Lett. B 700, 243-248 (2011) doi:10.1016/j.physletb.2011.04.063 [arXiv:1103.4107 [hep-th]].
  12. P. Basu and L. A. Pando Zayas, “Analytic Non-integrability in String Theory,” Phys. Rev. D 84, 046006 (2011) doi:10.1103/PhysRevD.84.046006 [arXiv:1105.2540 [hep-th]].
  13. P. Basu, D. Das, A. Ghosh and L. A. Pando Zayas, “Chaos around Holographic Regge Trajectories,” JHEP 05, 077 (2012) doi:10.1007/JHEP05(2012)077 [arXiv:1201.5634 [hep-th]].
  14. L. A. Pando Zayas and D. Reichmann, “A String Theory Explanation for Quantum Chaos in the Hadronic Spectrum,” JHEP 04, 083 (2013) doi:10.1007/JHEP04(2013)083 [arXiv:1209.5902 [hep-th]].
  15. P. Basu and A. Ghosh, “Confining Backgrounds and Quantum Chaos in Holography,” Phys. Lett. B 729, 50-55 (2014) doi:10.1016/j.physletb.2013.12.052 [arXiv:1304.6348 [hep-th]].
  16. P. Basu, P. Chaturvedi and P. Samantray, “Chaotic dynamics of strings in charged black hole backgrounds,” Phys. Rev. D 95, no.6, 066014 (2017) doi:10.1103/PhysRevD.95.066014 [arXiv:1607.04466 [hep-th]].
  17. K. L. Panigrahi and M. Samal, “Chaos in classical string dynamics in γ^^𝛾\hat{\gamma}over^ start_ARG italic_γ end_ARG deformed A⁢d⁢S5×T1,1𝐴𝑑subscript𝑆5superscript𝑇11AdS_{5}\times T^{1,1}italic_A italic_d italic_S start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × italic_T start_POSTSUPERSCRIPT 1 , 1 end_POSTSUPERSCRIPT,” Phys. Lett. B 761, 475-481 (2016) doi:10.1016/j.physletb.2016.08.021 [arXiv:1605.05638 [hep-th]].
  18. D. Giataganas, L. A. Pando Zayas and K. Zoubos, “On Marginal Deformations and Non-Integrability,” JHEP 01, 129 (2014) doi:10.1007/JHEP01(2014)129 [arXiv:1311.3241 [hep-th]].
  19. T. Ishii, S. Kushiro and K. Yoshida, “Chaotic string dynamics in deformed T1,1,” JHEP 05, 158 (2021) doi:10.1007/JHEP05(2021)158 [arXiv:2103.12416 [hep-th]].
  20. D. Roychowdhury, “Analytic integrability for strings on η𝜂\etaitalic_η and λ𝜆\lambdaitalic_λ deformed backgrounds,” JHEP 10, 056 (2017) doi:10.1007/JHEP10(2017)056 [arXiv:1707.07172 [hep-th]].
  21. C. Núñez, J. M. Penín, D. Roychowdhury and J. Van Gorsel, “‘The non-Integrability of Strings in Massive Type IIA and their Holographic duals,” JHEP 06, 078 (2018) doi:10.1007/JHEP06(2018)078 [arXiv:1802.04269 [hep-th]].
  22. C. Nunez, D. Roychowdhury and D. C. Thompson, “Integrability and non-integrability in 𝒩=2𝒩2\mathcal{N}=2caligraphic_N = 2 SCFTs and their holographic backgrounds,” JHEP 07, 044 (2018) doi:10.1007/JHEP07(2018)044 [arXiv:1804.08621 [hep-th]].
  23. A. Banerjee and A. Bhattacharyya, “Probing analytical and numerical integrability: the curious case of (AdS×5S5{}_{5}\times S^{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT)η,” JHEP 11, 124 (2018) doi:10.1007/JHEP11(2018)124 [arXiv:1806.10924 [hep-th]].
  24. K. S. Rigatos, “Nonintegrability of La,b,csuperscript𝐿𝑎𝑏𝑐L^{a,b,c}italic_L start_POSTSUPERSCRIPT italic_a , italic_b , italic_c end_POSTSUPERSCRIPT quiver gauge theories,” Phys. Rev. D 102, no.10, 106022 (2020) doi:10.1103/PhysRevD.102.106022 [arXiv:2009.11878 [hep-th]].
  25. D. Giataganas and K. Zoubos, “Non-integrability and Chaos with Unquenched Flavor,” JHEP 10, 042 (2017) doi:10.1007/JHEP10(2017)042 [arXiv:1707.04033 [hep-th]].
  26. K. Filippas, “Non-integrability on AdS3 supergravity backgrounds,” JHEP 02, 027 (2020) doi:10.1007/JHEP02(2020)027 [arXiv:1910.12981 [hep-th]].
  27. K. Filippas, “Nonintegrability of the ΩΩ\Omegaroman_Ω deformation,” Phys. Rev. D 101, no.4, 046025 (2020) doi:10.1103/PhysRevD.101.046025 [arXiv:1912.03791 [hep-th]].
  28. K. S. Rigatos, “Non-integrability in AdS3 vacua,” JHEP 02, 032 (2021) doi:10.1007/JHEP02(2021)032 [arXiv:2011.08224 [hep-th]].
  29. 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) doi:10.1103/PhysRevD.69.046002 [arXiv:hep-th/0305116 [hep-th]].
  30. G. Arutyunov and S. Frolov, “Superstrings on A⁢d⁢S4×C⁢P3𝐴𝑑subscript𝑆4𝐶superscript𝑃3AdS_{4}\times CP^{3}italic_A italic_d italic_S start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT × italic_C italic_P start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT as a Coset Sigma-model,” JHEP 09, 129 (2008) doi:10.1088/1126-6708/2008/09/129 [arXiv:0806.4940 [hep-th]].
  31. B. Stefanski, jr, “Green-Schwarz action for Type IIA strings on A⁢d⁢S4×C⁢P3𝐴𝑑subscript𝑆4𝐶superscript𝑃3AdS_{4}\times CP^{3}italic_A italic_d italic_S start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT × italic_C italic_P start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT,” Nucl. Phys. B 808, 80-87 (2009) doi:10.1016/j.nuclphysb.2008.09.015 [arXiv:0806.4948 [hep-th]].
  32. D. Sorokin and L. Wulff, “‘Evidence for the classical integrability of the complete A⁢d⁢S4×C⁢P3𝐴𝑑subscript𝑆4𝐶superscript𝑃3AdS_{4}\times CP^{3}italic_A italic_d italic_S start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT × italic_C italic_P start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT superstring,” JHEP 11, 143 (2010) doi:10.1007/JHEP11(2010)143 [arXiv:1009.3498 [hep-th]].
  33. K. Zarembo, “Strings on Semisymmetric Superspaces,” JHEP 05, 002 (2010) doi:10.1007/JHEP05(2010)002 [arXiv:1003.0465 [hep-th]].
  34. S. Frolov, “Lax pair for strings in Lunin-Maldacena background,” JHEP 05, 069 (2005) doi:10.1088/1126-6708/2005/05/069 [arXiv:hep-th/0503201 [hep-th]].
  35. J. J.  Kovacic, “An algorithm for solving second order linear homogeneous differential equations,” J. Symb. Comput. 2 (1986) 3.
  36. B.  D.  Saunders, “An implementation of Kovacic’s algorithm for solving second order linear homogeneous differential equations,” The Proceedings of the 4th ACM Symposium on Symbolic and Algebraic Computation, SYMSAC’81, August 5–7, Snowbird, USA, 1981.
  37. J. J.  Kovacic, “Picard-Vessiot Theory, Algebraic Groups and Group Schemes,” Department of Mathematics, the City College of the City University of New York, 2005.
  38. C. Núñez, D. Roychowdhury, S. Speziali and S. Zacarías, “Holographic aspects of four dimensional 𝒩=2𝒩2{\cal N}=2caligraphic_N = 2 SCFTs and their marginal deformations,” Nucl. Phys. B 943, 114617 (2019) doi:10.1016/j.nuclphysb.2019.114617 [arXiv:1901.02888 [hep-th]].
  39. J. Pal, S. Roychowdhury, A. Lala and D. Roychowdhury, “Integrability and non-integrability for marginal deformations of 4d 𝒩=2𝒩2\mathcal{N}=2caligraphic_N = 2 SCFTs,” JHEP 10, 173 (2023) doi:10.1007/JHEP10(2023)173 [arXiv:2307.12079 [hep-th]].
  40. D. E. Berenstein, J. M. Maldacena and H. S. Nastase, “Strings in flat space and pp waves from 𝒩=4𝒩4\mathcal{N}=4caligraphic_N = 4 superYang-Mills,” JHEP 04, 013 (2002) doi:10.1088/1126-6708/2002/04/013 [arXiv:hep-th/0202021 [hep-th]].
  41. Y. Lozano, C. Nunez and S. Zacarias, “BMN Vacua, Superstars and Non-Abelian T-duality,” JHEP 09, 008 (2017) doi:10.1007/JHEP09(2017)008 [arXiv:1703.00417 [hep-th]].
  42. H. Lin, “The Supergravity dual of the BMN matrix model,” JHEP 12, 001 (2004) doi:10.1088/1126-6708/2004/12/001 [arXiv:hep-th/0407250 [hep-th]].
  43. H. Lin and J. M. Maldacena, “Fivebranes from gauge theory,” Phys. Rev. D 74, 084014 (2006) doi:10.1103/PhysRevD.74.084014 [arXiv:hep-th/0509235 [hep-th]].
  44. H. Lin, O. Lunin and J. M. Maldacena, “Bubbling AdS space and 1/2 BPS geometries,” JHEP 10, 025 (2004) doi:10.1088/1126-6708/2004/10/025 [arXiv:hep-th/0409174 [hep-th]].
  45. D. Roychowdhury, “Matrix model correlators from non-Abelian T-dual 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,” JHEP 02, 062 (2024) doi:10.1007/JHEP02(2024)062 [arXiv:2310.10210 [hep-th]].
  46. R. Hilborn, “Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers”, Oxford University Press, second edition ed., 2000.
  47. E. Ott, “Chaos in Dynamical Systems”, Cambridge University Press, second edition ed., 2002.
  48. Y. Asano, D. Kawai and K. Yoshida, “Chaos in the BMN matrix model,” JHEP 06, 191 (2015) doi:10.1007/JHEP06(2015)191 [arXiv:1503.04594 [hep-th]].
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