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Stability Longevity and All That: False Vacua and Topological Defects

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Gravity and the Quantum

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 187))

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Abstract

I present two interesting studies related to the role of solitons in theories with spontaneous symmetry breaking. Quantised fermions coupled to solitons are known to induce fractional fermion number. I present an example where an unstable topological solution binding a zero mode of a majorana fermion gets stabilised due to the induced fractional number. Thus neither is the cosmic string stable nor is the fermion number conserved, yet the bound state then becomes stable due to Quantum Mechanics. The other phenomenon concerns a metastable vacuum getting destabilised due to the presence of a cosmic string. This happens because the scalar field signalling spontaneous symmetry breaking acquires a vacuum expectation value approaching its true vacuum value in the core of the string. Thus the string acts like a seed nucleating the true vacuum. The instanton mediating between the false vacuum and the exit point into the true vacuum is shown to exist and graphically displayed through a numeric calculation. T. Padmanabhan has been a long time friend and was collaborator for early investigations in this direction. I review these works done subsequently with other collaborators as a felicitation to him on his sixtieth birthday.

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References

  1. U.A. Yajnik, Phys. Rev. D 34, 1237 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  2. U.A. Yajnik, T. Padmanabhan, Phys. Rev. D 35, 3100 (1987)

    Article  ADS  Google Scholar 

  3. U.A. Yajnik, Phys. Lett. B 234, 271 (1990)

    Article  ADS  Google Scholar 

  4. N. Sahu, U.A. Yajnik, Phys. Lett. B 596, 1 (2004). arXiv:hep-th/0405140

    Article  ADS  MathSciNet  Google Scholar 

  5. B.H. Lee, W. Lee, R. MacKenzie, M.B. Paranjape, U.A. Yajnik, D.h. Yeom, Phys. Rev. D 88(10), 105008 (2013). arXiv:1310.3005 [hep-th]

  6. R. MacKenzie, F. Wilczek, Phys. Rev. D 30, 2194 (1984)

    Article  ADS  Google Scholar 

  7. B.H. Lee, W. Lee, R. MacKenzie, M.B. Paranjape, U.A. Yajnik, D.h Yeom, Phys. Rev. D 88, 085031 (2013)

    Article  ADS  Google Scholar 

  8. H.B. Nielsen, P. Olesen, Nucl. Phys. B 61, 45 (1973)

    Article  ADS  Google Scholar 

  9. A. Abrikozov, JETP (Sov. Phys.) 5, 1173 (1957)

    Google Scholar 

  10. R. Jackiw, C. Rebbi, Phys Rev. D 13, 3398 (1976)

    Google Scholar 

  11. R. Jackiw, Rev. Mod. Phys. 49, 681 (1977)

    Article  ADS  Google Scholar 

  12. H. de Vega, Phys. Rev. D 18, 2932 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  13. A. Stern, Phys. Rev. Lett. 52, 2118 (1983)

    Article  ADS  Google Scholar 

  14. A. Stern, U.A. Yajnik, Nucl. Phys. B 267, 158 (1986)

    Article  ADS  Google Scholar 

  15. S.C. Davis, A.C. Davis, W.B. Perkins, Phys. Lett. B 408, 81 (1997)

    Article  ADS  Google Scholar 

  16. A.C. Davis, S.C. Davis, W.B. Perkins, in Proceedings of COSMO99. arXiv:hep-ph/0005091

  17. A.C. Davis, T.W.B. Kibble, M. Pickles, D.A. Steer, Phys. Rev. D 62, 083516 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  18. G.C. Wick, A.S. Wightman, E.P. Wigner, Phys. Rev. 88, 101 (1952)

    Article  ADS  Google Scholar 

  19. S. Weinberg, The Quantum Theory of Fields, vol. I, sec. 3.3 (Cambridge University Press, Cambridge, 1996)

    Book  MATH  Google Scholar 

  20. J. Preskill, A. Vilenkin, Phys. Rev. D 47, 2324 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  21. R. Slansky, Phys. Rep. 79, 1 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  22. E.J. Weinberg, Phys. Rev. D 24, 2669 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  23. N. Ganoulis, G. Lazarides, Phys. Rev. D 38, 547 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  24. R. Jackiw, P. Rossi, Nucl. Phys. B 190, 681 (1981)

    Article  ADS  Google Scholar 

  25. E.C.G. Sudarshan, U.A. Yajnik, Phys. Rev. D 33, 1830 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  26. See for instance M. Fukugita, T. Yanagida, in Physics and Astrophysics of Neutrinos, ed. by M. Fukugita, A. Suzuki (Springer, Berlin, 1994), pp. 1–248

    Google Scholar 

  27. B. Kumar, M.B. Paranjape, U.A. Yajnik, Phys. Rev. D 82, 025022 (2010)

    Article  ADS  Google Scholar 

  28. B. Kumar, U.A. Yajnik, Nucl. Phys. B 831, 162 (2010)

    Article  ADS  Google Scholar 

  29. A. Aguirre, M.C. Johnson, M. Larfors, Phys. Rev. D 81, 043527 (2010)

    Article  ADS  Google Scholar 

  30. M. Haberichter, R. MacKenzie, M.B. Paranjape, Y. Ung, J. Math. Phys. 57(4), 042303 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  31. É. Dupuis, Y. Gobeil, R. MacKenzie, L. Marleau, M.B. Paranjape, Y. Ung, Phys. Rev. D 92(2), 025031 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  32. M. Eto, Y. Hamada, K. Kamada, T. Kobayashi, K. Ohashi, Y. Ookouchi, JHEP 1303, 159 (2013)

    Article  ADS  Google Scholar 

  33. K. Kamada, T. Kobayashi, K. Ohashi, Y. Ookouchi, JHEP 1305, 091 (2013)

    Article  ADS  Google Scholar 

  34. A. Kasai, Y. Nakai, Y. Ookouchi, JHEP 1606, 029 (2016)

    Article  ADS  Google Scholar 

  35. A. Kasai, Y. Ookouchi, JHEP 1506, 098 (2015)

    Article  ADS  Google Scholar 

  36. A. Kasai, Y. Ookouchi, Phys. Rev. D 91(12), 126002 (2015)

    Article  ADS  Google Scholar 

  37. B.H. Lee, W. Lee, D.h. Yeom. Phys. Rev. D 92(2), 024027 (2015)

    Google Scholar 

  38. B. Garbrecht, P. Millington, Phys. Rev. D 92, 125022 (2015)

    Article  ADS  Google Scholar 

  39. Y. Nakai, Y. Ookouchi, arXiv:1608.01232 [hep-th]

  40. P.J. Steinhardt, Phys. Rev. D 24, 842 (1981)

    Article  ADS  Google Scholar 

  41. S.R. Coleman, Phys. Rev. D 15, 2929 (1977); C.A. Callan, S. Coleman, Phys. Rev. D 16, 1762 (1977)

    Google Scholar 

  42. B. Kumar, U.A. Yajnik, Phys. Rev. D 79, 065001 (2009)

    Article  ADS  Google Scholar 

  43. T.W.B. Kibble, J. Phys. A 9, 1387 (1976); T.W.B. Kibble, Phys. Rep. 67, 183 (1980); W.H. Zurek, Nature (London) 317, 505 (1985); W.H. Zurek, Acta Phys. Pol. B 24, 1301 (1993)

    Google Scholar 

  44. U.A. Yajnik, H. Widyan, D. Choudhari, S. Mahajan, A. Mukherjee, Phys. Rev. D 59, 103508 (1999)

    Article  ADS  Google Scholar 

  45. S.C. Davis, W.B. Perkins, A.C. Davis, Phys. Rev. D 62, 043503 (2000)

    Article  ADS  Google Scholar 

  46. S.A. Abel, C.-S. Chu, J. Jaeckel, V.V. Khoze, JHEP 0701, 089 (2007). arXiv:hep-th/0610334; W. Fischler, V. Kaplunovsky, L. Mannelli, M. Torres, C. Krishnan, JHEP 03, 107 (2007)

  47. S. Kachru, R. Kallosh, A.D. Linde, S.P. Trivedi, Phys. Rev. D 68, 046005 (2003). arXiv:hep-th/0301240

    Article  ADS  MathSciNet  Google Scholar 

  48. N.W. Ashcroft, N.D. Mermin, Solid State Physics (Harcourt College Publishers, 1976)

    Google Scholar 

  49. A.J. Dolgert, S.J. Di Bartolo, A.T. Dorsey, Phys. Rev. B 53, 5650 (1996)

    Article  ADS  Google Scholar 

  50. Superconductive Particle Detectors, ed. by A. Barone (World Scientific, Singapore, 1987); K. Pretzl, J. Low Temp. Phys. 93, 439 (1993)

    Google Scholar 

  51. A.J. Leggett, A theoretical description of the new phases of liquid 3He. Rev. Mod. Phys. 47, 331 (1975)

    Google Scholar 

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Acknowledgements

I thank the editors of this volume for giving me the opportunity to contribute. This article is patched together from [4, 5], and it is a pleasant duty to acknowledge the partnership of the coauthors of both the papers where the work was originally reported. I also acknowledge the support of the Department of Science and Technology, India, and the Ministère des relations internationales du Québec.

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  1. Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Urjit A. Yajnik

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Correspondence to Urjit A. Yajnik .

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  1. Department of Physical Sciences, IISER Mohali, Mohali, Punjab, India

    Jasjeet Singh Bagla

  2. Ryussi Technologies Pvt. Ltd., Pune, India

    Sunu Engineer

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Yajnik, U.A. (2017). Stability Longevity and All That: False Vacua and Topological Defects. In: Bagla, J., Engineer, S. (eds) Gravity and the Quantum. Fundamental Theories of Physics, vol 187. Springer, Cham. https://doi.org/10.1007/978-3-319-51700-1_28

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