Abstract
We study the effect of vortices on the tunneling decay of a symmetry-breaking false vacuum in three spacetime dimensions with gravity. The scenario considered is one in which the initial state, rather than being the homogeneous false vacuum, contains false vortices. The question addressed is whether, and, if so, under which circumstances, the presence of vortices has a significant catalyzing effect on vacuum decay. After studying the existence and properties of vortices, we study their decay rate through quantum tunneling using a variety of techniques. In particular, for so-called thin-wall vortices we devise a one-parameter family of configurations allowing a quantum-mechanical calculation of tunneling. Also for thin-wall vortices, we employ the Israel junction conditions between the interior and exterior spacetimes. Matching these two spacetimes reveals a decay channel which results in an unstable, expanding vortex. We find that the tunneling exponent for vortices, which is the dominant factor in the decay rate, is half that for Coleman-de Luccia bubbles. This implies that vortices are short-lived, making them cosmologically significant even for low vortex densities. In the limit of the vanishing gravitational constant we smoothly recover our earlier results for the decay of the false vortex in a model without gravity.
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References
A.A. Abrikosov, On the Magnetic properties of superconductors of the second group, Sov. Phys. JETP 5 (1957) 1174 [INSPIRE].
H.B. Nielsen and P. Olesen, Vortex Line Models for Dual Strings, Nucl. Phys. B 61 (1973) 45 [INSPIRE].
T.W.B. Kibble, Topology of Cosmic Domains and Strings, J. Phys. A 9 (1976) 1387 [INSPIRE].
T.W.B. Kibble, Some Implications of a Cosmological Phase Transition, Phys. Rept. 67 (1980) 183 [INSPIRE].
R.H. Brandenberger, Searching for Cosmic Strings in New Observational Windows, Nucl. Phys. Proc. Suppl. 246-247 (2014) 45 [ar**v:1301.2856] [INSPIRE].
H. Tashiro, T. Sekiguchi and J. Silk, High redshift signatures in the 21 cm forest due to cosmic string wakes, JCAP 01 (2014) 013 [ar**v:1310.4176] [INSPIRE].
B.-H. Lee, W. Lee, R. MacKenzie, M.B. Paranjape, U.A. Yajnik and D.-h. Yeom, Tunneling decay of false vortices, Phys. Rev. D 88 (2013) 085031 [ar**v:1308.3501] [INSPIRE].
S. Deser, R. Jackiw and G. ’t Hooft, Three-Dimensional Einstein Gravity: Dynamics of Flat Space, Annals Phys. 152 (1984) 220 [INSPIRE].
E.W. Hirschmann and D.L. Welch, Magnetic solutions to (2+1) gravity, Phys. Rev. D 53 (1996) 5579 [hep-th/9510181] [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. D 16 (1977) 1248] [INSPIRE].
C.G. Callan Jr. and S.R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE].
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44S10 (1966) 1 [Erratum ibid. B 48 (1967) 463] [INSPIRE].
J.W. York Jr., Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman and Company, New York (1973).
B. Kumar, M.B. Paranjape and U.A. Yajnik, Fate of the false monopoles: Induced vacuum decay, Phys. Rev. D 82 (2010) 025022 [ar**v:1006.0693] [INSPIRE].
D. Garfinkle, General Relativistic Strings, Phys. Rev. D 32 (1985) 1323 [INSPIRE].
A. Vilenkin, Cosmic Strings and Domain Walls, Phys. Rept. 121 (1985) 263 [INSPIRE].
P. Laguna-Castillo and R.A. Matzner, Coupled Field Solutions for U(1) Gauge Cosmic Strings, Phys. Rev. D 36 (1987) 3663 [INSPIRE].
V.A. Rubakov, Classical theory of gauge fields, Princeton University, Princeton, NJ (2002).
S.R. Coleman, V. Glaser and A. Martin, Action Minima Among Solutions to a Class of Euclidean Scalar Field Equations, Commun. Math. Phys. 58 (1978) 211 [INSPIRE].
P.J. Steinhardt, Monopole and Vortex Dissociation and Decay of the False Vacuum, Nucl. Phys. B 190 (1981) 583 [INSPIRE].
J. Hong, Y. Kim and P.Y. Pac, On the Multivortex Solutions of the Abelian Chern-Simons-Higgs Theory, Phys. Rev. Lett. 64 (1990) 2230 [INSPIRE].
R. Jackiw and E.J. Weinberg, Selfdual Chern-Simons Vortices, Phys. Rev. Lett. 64 (1990) 2234 [INSPIRE].
C.-k. Lee, K.-M. Lee and E.J. Weinberg, Supersymmetry and Selfdual Chern-Simons Systems, Phys. Lett. B 243 (1990) 105 [INSPIRE].
B.-H. Lee, C.-k. Lee and H. Min, Supersymmetric Chern-Simons vortex systems and fermion zero modes, Phys. Rev. D 45 (1992) 4588 [INSPIRE].
I. Cho, T. Kim, Y. Kim and K. Ryu, Relativistic Dynamics of Multi-BPS D-vortices and Straight BPS D-strings, Phys. Lett. B 666 (2008) 502 [ar**v:0707.0357] [INSPIRE].
C. Kim, Y. Kim, O.-K. Kwon and H. Nakajima, Vortex-type Half-BPS Solitons in ABJM Theory, Phys. Rev. D 80 (2009) 045013 [ar**v:0905.1759] [INSPIRE].
É. Dupuis, Y. Gobeil, R. MacKenzie, L. Marleau, M.B. Paranjape and Y. Ung, Tunneling decay of false kinks, Phys. Rev. D 92 (2015) 025031 [ar**v:1506.05091] [INSPIRE].
M. Haberichter, R. MacKenzie, M.B. Paranjape and Y. Ung, Tunneling decay of false domain walls: the silence of the lambs, J. Math. Phys. 57 (2016) 042303 [ar**v:1506.05838] [INSPIRE].
B.-H. Lee, W. Lee, R. MacKenzie, M.B. Paranjape, U.A. Yajnik and D.-h. Yeom, Battle of the bulge: Decay of the thin, false cosmic string, Phys. Rev. D 88 (2013) 105008 [ar**v:1310.3005] [INSPIRE].
U.A. Yajnik, Phase transition induced by cosmic strings, Phys. Rev. D 34 (1986) 1237 [INSPIRE].
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Dupuis, É., Gobeil, Y., Lee, BH. et al. Tunneling decay of false vortices with gravitation. J. High Energ. Phys. 2017, 28 (2017). https://doi.org/10.1007/JHEP11(2017)028
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DOI: https://doi.org/10.1007/JHEP11(2017)028