\begin{document}$AdS_4 \times S^7/Z_k$\end{document} background and setting the internal space as an \begin{document}$S^1$\end{document} Hopf fibration on \begin{document}$CP^3$\end{document}, we obtain a consistent truncation. The (pseudo)scalars, in the resulting scalar equations in Euclidean AdS\begin{document}$_4$\end{document}space, may be considered to arise from (anti)M-branes wrapping around the internal directions in the (Wick-rotated) skew-whiffed M2-brane background (as the resulting theory is for anti-M2-branes), thus realizing the modes after swapping the three fundamental representations \begin{document}${\bf{8}}_s$\end{document}, \begin{document}${\bf{8}}_c$\end{document}, and \begin{document}${\bf{8}}_v$\end{document} of \begin{document}$S O(8)$\end{document}. Taking the backreaction on the external and internal spaces, we obtain the massless and massive modes, corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT\begin{document}$_3$\end{document}, respectively. Subsequently, we obtain a closed solution for the bulk equation and compute its correction with respect to the background action. Next, considering the Higgs-like (breathing) mode \begin{document}$m^2=18$\end{document}, having all supersymmetries as well as parity and scale-invariance broken, solving the associated bulk equation with mathematical methods, specifically the Adomian decomposition method, and analyzing the behavior near the boundary of the solutions, we realize the boundary duals in the \begin{document}$S U(4) \times U(1)$\end{document}-singlet sectors of the ABJM model. Then, introducing the new dual deformation \begin{document}$\Delta_+ = 3, 6$\end{document} operators made of bi-fundamental scalars, fermions, and \begin{document}$U(1)$\end{document} gauge fields, we obtain the \begin{document}$S O(4)$\end{document}-invariant solutions as small instantons on a three-sphere with the radius at infinity, which correspond to collapsing bulk bubbles leading to big-crunch singularities."> Higgs-like (pseudo)scalars in AdS<sub>4</sub>, marginal and irrelevant deformations in CFT<sub>3</sub>, and instantons on <i>S</i><sup>3</sup> -
  • [1]

    M. Naghdi, Class. Quant. Grav.33, 115005 (2016), arXiv:1505.00179[hep-th]

  • [2]

    M. Naghdi, Eur. Phys. J. Plus133, 307 (2018), arXiv:1703.02765[hep-th]

  • [3]

    M. Naghdi, Fortschr. Phys. 1800044 (2018), arXiv:1708.02530[hep-th]

  • [4]

    M. Naghdi, Eur. Phys. J. Plus138, 45 (2023), arXiv:2002.06547[hep-th]

  • [5]

    M. Naghdi, Eur. Phys. J. Plus138, 300 (2023), arXiv:2005.00358[hep-th]

  • [6]

    O. Aharony, O. Bergman, D. L. Jafferiset al., JHEP0810, 091 (2008), arXiv:0806.1218[hep-th]

  • [7]

    M. J. Duff and C. N. Pope, Nucl. Phys. B255, 355 (1985)

  • [8]

    M. Bremer, M. J. Duff, H. Luet al., Nucl. Phys. B543, 321 (1999), arXiv:hep-th/9807051

  • [9]

    M. J. Duff and J. T. Liu, Nucl. Phys. B554, 273 (1999), arXiv:hep-th/9901149

  • [10]

    J. P. Gauntlett, S. Kim, O. Varelaet al., JHEP0904, 102 (2009), arXiv:0901.0676[hep-th]

  • [11]

    S. W. Hawking and H. S. Reall, Phys. Rev. D59, 023502 (1998), arXiv:hep-th/9807100

  • [12]

    D. Bak and S. Yun, Class. Quant. Grav.27, 215011 (2010), arXiv:1001.4089[hep-th]

  • [13]

    G. Adomian,"Solving frontier problems of physics: The decomposition method", Springer, 1st Edition (1994)

  • [14]

    A. C. Petkou, JHEP0303, 049 (2003), arXiv:hep-th/0302063

  • [15]

    M. Naghdi, Iran. J. Phys. Res.20, 471 (2020)

  • [16]

    M. Naghdi, Phys. Rev. D88, 026013 (2013), arXiv:1302.5294[hep-th]

  • [17]

    M. Naghdi, Eur. Phys. J. C74, 2826 (2014), arXiv:1302.5534[hep-th]

  • [18]

    E. Witten, Adv. Theor. Math. Phys.2, 253 (1998), arXiv:hep-th/9802150

  • [19]

    D. Z. Freedman, S. D. Mathur, A. Matusiset al., Nucl. Phys. B546, 96 (1999), arXiv:hep-th/9804058

  • [20]

    M. Bianchi, D. Z. Freedman, and K. Skenderis, Nucl. Phys. B631, 159 (2002), arXiv:hep-th/0112119

  • [21]

    Y. A. Kubyshin and P. G. Tinyakov, Phys. Rev. D65, 085007 (2002), arXiv:hep-ph/0010226

  • [22]

    A. D. Polyanin and V. F. Zaitsev,Handbook of Nonlinear Partial Differential Equations(Chapman and Hall/CRC Press, 2nd Edition, 2012)

  • [23]

    M. J. Duff, B. E. W. Nilsson, and C. N. Pope, Nucl. Phys. B233, 433 (1984)

  • [24]

    D. N. Page and C. N. Pope, Phys. Lett. B145, 333 (1984)

  • [25]

    X. Chu, H. Nastase, B. Nilssonet al., JHEP1104, 040 (2011), arXiv:1012.5969[hep-th]

  • [26]

    O. Aharony, O. Bergman, D. L. Jafferis, JHEP0811, 043 (2008), arXiv:0807.4924[hep-th]

  • [27]

    W. Heidenreich, Phys. Lett. B110, 461 (1982)

  • [28]

    F. Englert and H. Nicolai,Supergravity in eleven-dimensional space-time, Part of Group Theoretical Methods in Physics, pp 249–283 (1983)

  • [29]

    E. Sezgin, Phys. Lett. B138, 57 (1984)

  • [30]

    B. Biran, A. Casher, F. Englertet al., Phys. Lett. B134, 179 (1984)

  • [31]

    A. Casher, F. Englert, H. Nicolaiet al., Nucl. Phys. B243, 173 (1984)

  • [32]

    M. J. Duff, B. E. W. Nilsson, and C. N. Pope, Phys. Rept.130, 1 (1986)

  • [33]

    E. Halyo, JHEP9804, 011 (1998), arXiv:hep-th/9803077

  • [34]

    E. D'Hoker and B. Pioline, JHEP0007, 021 (2000), arXiv:hep-th/0006103

  • [35]

    M. Bianchi, R. Poghossian, and M. Samsonyan, JHEP1010, 021 (2010), arXiv:1005.5307[hep-th]

  • [36]

    D. Forcella and A. Zaffaroni, arXiv: 1103.0648[hep-th], arXiv:1103.0648[hep-th]

  • [37]

    N. Bobev and P. Bomans, JHEP02, 052 (2022), arXiv:2112.10532[hep-th]

  • [38]

    B. E. W. Nilsson and C. N. Pope, Class. Quant. Grav.1, 499 (1984)

  • [39]

    A. Gustavsson and S. J. Rey, arXiv: 0906.3568[hep-th]

  • [40]

    I. R. Klebanov and E. Witten, Nucl. Phys. B556, 89 (1999), arXiv:hep-th/9905104

  • [41]

    V. Balasubramanian, P. Kraus, A. Lawrence, and S. Trivedi, Phys. Rev. D59, 104021 (1999), arXiv:hep-th/9808017

  • [42]

    P. Breitenlohner and D. Z. Freedman, Phys. Lett. B115, 197 (1982)

  • [43]

    M. J. Duff, B. E. W. Nilsson and C. N. Pope, Phys. Lett. B139, 154 (1984)

  • [44]

    M. A. Vasiliev, J. Phys. A46, 214013 (2013), arXiv:1203.5554[hep-th]

  • [45]

    M. Naghdi, Class. Quant. Grav.32, 215018 (2015), arXiv:1502.03281[hep-th]

  • [46]

    K. G. Akdeniz and A. Smailagić, Nuovo Cim. A51, 345 (1979)

  • [47]

    R. D. Pisarski, Phys. Rev. Lett.48, 574 (1982)

  • [48]

    W. A. Bardeen, M. Moshe, and M. Bander, Phys. Rev. Lett.52, 1188 (1984)

  • [49]

    I. Papadimitriou, JHEP0702, 008 (2007), arXiv:hep-th/0606038

  • [50]

    B. Craps, T. Hertog, and N. Turok, Phys. Rev. D80, 086007 (2009), arXiv:0905.0709[hep-th]

  • [51]

    J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonket al., JHEP0809, 113 (2008), arXiv:0807.1074[hep-th]

  • [52]

    I. Arav, J. P. Gauntlett, M. Robertset al., JHEP1904, 099 (2019), arXiv:1812.11159[hep-th]

  • [53]

    K. K. Kim, Y. Kim, O-K. Kwonet al., arXiv: 1910.05044[hep-th]

  • [54]

    I. Affleck, Nucl. Phys. B191, 429 (1981)

  • [55]

    M. Nielsen and N. K. Nielsen, Phys. Rev. D61, 105020 (2000), arXiv:hep-th/9912006

  • [56]

    P. M. Glerfoss and N. K. Nielsen, Annals Phys.321, 331 (2006), arXiv:hep-th/0504178

  • [57]

    A. A. Belavin, A. M. Polyakov, A. S. Shvartset al., Phys. Lett. B59, 85 (1975)

  • [58]

    G. 't Hooft, Phys. Rev. D14, 3432 (1978)

  • [59]

    S. Fubini, Nuovo Cim. A34, 521 (1976)

  • [60]

    L. N. Lipatov, Sov. Phys. JETP45, 216 (1977)

  • [61]

    E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, Phys. Rev. D15, 1544 (1977)

  • [62]

    A. J. McKane and D. J. Wallace, J. Phys. A11, 2285 (1978)

  • [63]

    A. Actor, Fortschr. Phys.30, 437 (1982)

  • [64]

    V. de Alfaro, S. Fubini, and G. Furlan, Phys. Lett. B65, 163 (1976)

  • [65]

    E. Corrigan and D. B. Fairlie, Phys. Lett. B67, 69 (1977)

  • [66]

    S. Choudhury, A. Dey, I. Halderet al., JHEP1811, 177 (2018), arXiv:1804.08635[hep-th]

  • [67]

    O. Aharony, S. Jain, and Sh. Minwalla, JHEP1812, 058 (2018), arXiv:1808.03317[hep-th]

  • [68]

    Sh. Minwalla and Sh. Yokoyama, JHEP1602, 103 (2016), arXiv:1507.04546[hep-th]

  • [69]

    S. Giombi, V. Gurucharan, V. Kirilinet al., JHEP1701, 058 (2017), arXiv:1610.08472[hep-th]

  • [70]

    S. R. Coleman and F. De Luccia, Phys. Rev. D21, 3305 (1980)

  • [71]

    L. F. Abbott and S. Coleman, Nucl. Phys. B259, 4170 (1985)

  • [72]

    T. Hertog and G. T. Horowitz, JHEP04, 005 (2005), arXiv:hep-th/0503071

  • [73]

    B. Craps, T. Hertog, and N. Turok, Phys. Rev. D86, 043513 (2012), arXiv:0712.4180[hep-th]

  • [74]

    J. L. F. Barbon and E. Rabinovici, JHEP1104, 044 (2011), arXiv:1102.3015[hep-th]

  • [75]

    J. Maldacena, arXiv: 1012.0274[hep-th]

  • [76]

    I. Bena, Phys. Rev. D62, 126006 (2000), arXiv:hep-th/000414

  • [77]

    J. Garriga, Prog. Theor. Phys. Suppl.190, 261 (2011), arXiv:1012.5996[hep-th]

  • [78]

    W. Lee, B.-H. Lee, Ch. H. Leeet al., Phys. Rev. D74, 123520 (2006), arXiv:hep-th/0604064

  • [79]

    A.-M. Wazwaz,Partial Differential Equations and Solitary Waves Theory(Springer, 1nd Edition, 2009)

Baidu
map