Iranian Journal of Physics Research

Instanton solutions in a model of AdS4/CFT3 correspondence

Document Type : Original Article

Author

M Naghdi

Department of Physics, Faculty of Basic Sciences, University of Ilam, Ilam ‎

https://doi.org/10.47176/ijpr.20.3.51063
Abstract
From the wrapping of the (anti)membranes of 11-dimensional supergravity over , on the internal directions along with an ansatz for its 4-form flux, by  solving the original equations and identities, we arrive at scalar differential equations in the  Euclidean  space; note that the associated bulk solutions and setups break all supersymmeties, parity and scale invariance; the resulting (pseudo) scalar potential, which is Higgs-like with two nearly homogeneous vacua, provides the first-order phase transition and tunneling from the false- to true- vacuum.  Here, concentrating on the three (pseudo) scalar modes m2=-2, 4, 10 , which are, in turn, realizable in Wick-rotated and skew-whiffed M2-branes backgrounds, we employ approximate methods and, particularly, Adomian decomposition method to solve the nonlinear second-order partial differential equations, valid in the  probe approximation, with the  Dirichlet boundary condition or the initial data from a basic exact solution, to get solutions in series expansions near the boundary in different orders of perturbation. Next, making use of the AdS4/CFT3 correspondence rules, after swapping the three fundamental representations of  for gravitino, we build the dual singlet  operators from the (scalar, fermion and gauge) fields in a 3-dimensional Chern-Simons-matter  gauge field theory living on the resultant anti-M2-brnaes; after that, by deforming the corresponding boundary actions with the operators, we get   invariant solutions with nonzero finite actions, which ,in turn, are small instantons sitting at the origin of a 3-sphere at infinity, causing  instability and mediating false vacuum decay. In other words, the boundary potentials unbounded from below are duals for the collapse of the bulk (thin-wall) vacuum bubbles and big crunch singularities.
 

Keywords

AdS4/CFT3 correspondence
(pseudo) scalar equations
adomian decomposition method
dual operators
instanton solutions
  1. J Maldacena, Adv. Theor. Math. Phys. 2 (1998) 231.‎

  2. I R Klebanov and E. Witten, Nucl. Phys. B 556 (1999) 89.‎

  3. O Aharony, O Bergman, D L Jafferis, and J Maldacena, JHEP 0810 (2008) 091. ‎

  4. M Naghdi, Int. J. Mod. Phys. A 26 (2011) 3259. ‎

  5. M Naghdi, Phys. Rev. D 88 (2013) 026013. ‎

  6. M Naghdi, Class. Quant. Grav. 32 (2015) 215018. ‎

  7. S Vandoren and P Nieuwenhuizen, [arXiv:0802.1862 [hep-th]].‎

  8. M Naghdi, Fortschr. Phys. 67 (2018) 1800044. ‎

  9. M Naghdi, [arXiv:2002.06547 [hep-th]].‎


10. T Hertog and G T Horowitz, JHEP 04 (2005)‎‏ ‏‎005 .‎


11. M Smolkin and N Turok, [arXiv:1211.1322 [hep-th]].‎


12. M Naghdi, [arXiv:2005.00358 [hep-th]].‎


13. S R Coleman and F. De Luccia, Phys. Rev. D 21 (1980) 3305.‎


14. M Naghdi, Eur. Phys. J. Plus 133 (2018) 307. ‎


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


16. E Witten, Adv. Theor. Math. Phys. 2 (1998) 253.‎


17. I Papadimitriou, JHEP 0705 (2007) 075.‎


18. A Imaanpur and M Naghdi, Phys. Rev. D 83 (2011) 085025.‎


19. M Naghdi, Class. Quant. Grav. 33 (2016) 115005.‎


20. O Hrycyna, Phys. Lett. B 768 (2017) 218. ‎


21. E Bergshoeff, M de Roo, E Eyras, B Janssen, and J P van der Schaar, Nucl. Phys. B 494 (1997) 119.‎


22. M J Duff, B E W Nilsson and C N Pope, Nucl. Phys. B 233 (1984) 433.‎


23. S Fubini, Nuovo Cim. A 34 (1976) 521.‎


24. F Loran, Mod. Phys. Lett. A 22 (2007) 2217. ‎


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


26. M Bianchi, R Poghossian and M Samsonyan, JHEP 1010 (2010) 021.‎


27. X Chu, H Nastase, B Nilsson, and C Papageorgakis, JHEP 1104 (2011) 040.‎


28. I Bena, Phys. Rev. D 62 (2000) 126006.‎


29. O Aharony, O Bergman, D L Jafferis, JHEP 0811 (2008) 043.‎


30. V Balasubramanian, P Kraus and A Lawrence, Phys. Rev. D 59 (1999) 046003.‎


31. P Breitenlohner and D Z Freedman, Phys. Lett. B 115 (1982) 197.‎


32. S Terashima, JHEP 0808 (2008) 080. ‎


33. B Craps, T Hertog and N Turok, Phys. Rev. D 80 (2009) 086007, ‎


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


35. S Elitzur, A Giveon, M Porrati and E Rabinovici, JHEP 0602 (2006) 006.‎


36. E Rabinovici and M Smolkin, JHEP 1107 (2011) 040.‎


37. I R Klebanov and A M Polyakov, Phys. Lett. B 550 (2002) 213. ‎


38. E Sezgin and P Sundell, Nucl. Phys. B 644 (2002) 303. [arXiv:hep-th/0205131], Erratum: Nucl. Phys. ‎B 660, 403 (2003).‎


39. E Sezgin and P Sundell, JHEP 0507 (2005) 044.  ‎


40. S Choudhury, A Dey, I Halder, S Jain, L Janagal, Sh Minwalla, and N Prabhakar, JHEP 1811‎‎(2018) 177.‎


41. O Aharony, S Jain and Sh Minwalla, JHEP 1812 (2018) 058. ‎


42. D Gaiotto and X Yin, JHEP 0708 (2007) 056.


43. O Aharony, G G Ari and R Yacoby, JHEP 1203 (2012) 037. ‎


44. I Affleck, Nucl. Phys. B 191 (1981) 429.‎


45. J Zinn-Justin, "The principles of instanton calculus: A few applications", Recent Advances in Field ‎Theory, Les Houches, Session XXXIX, edited by J.-B. Zuber and R. Stora (North Holland, ‎Amsterdam), (1982) ‎.


46. K G Akdeniz and A Smailagić, Nuovo Cim. A 51 (1979) 345.‎


47. A A Belavin, A M Polyakov, A S Shvarts and Yu S Tyupkin, Phys. Lett. B 59 (1975) 85.‎


48. L N Lipatov, Sov. Phys. JETP 45 (1977) 216, Zh. Eksp. Teor. Fiz. 72 (1977) 411.‎


49. S Coleman, V Glaser and A Martin, Commun. Math. Phys. 58 (1978) 211.‎


50. J L F Abbott and S Coleman, Nucl. Phys.‎‏ ‏B 259 (1985) 4170.‎


51. H Widyan, A Mukherjee, N Panchapakesan, and R P Saxena, Phys. Rev. D 59 (1999) 045003.‎


52. B H Lee, Ch H Lee, W Lee and Ch Oh, Phys. Rev. D 82 (2010) 024019.‎


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


54. J L F Barbon and E Rabinovici, JHEP 1104 (2011) 044.‎


55. L H Ooguri and C Vafa, Adv. Theor. Math. Phys. 21 (2017) 1787.

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