Abstract
We study the nonperturbative quantum evolution of the interacting O(N ) vector model at large-N , formulated on a spatial two-sphere, with time dependent couplings which diverge at finite time. This model - the so-called “E-frame” theory, is related via a conformal transformation to the interacting O(N ) model in three dimensional global de Sitter spacetime with time independent couplings. We show that with a purely quartic, relevant deformation the quantum evolution of the E-frame model is regular even when the classical theory is rendered singular at the end of time by the diverging coupling. Time evolution drives the E-frame theory to the large-N Wilson-Fisher fixed point when the classical coupling diverges. We study the quantum evolution numerically for a variety of initial conditions and demonstrate the finiteness of the energy at the classical “end of time”. With an additional (time dependent) mass deformation, quantum backreaction lowers the mass, with a putative smooth time evolution only possible in the limit of infinite quartic coupling. We discuss the relevance of these results for the resolution of crunch singularities in AdS geometries dual to E-frame theories with a classical gravity dual.
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References
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [INSPIRE].
T. Hertog and G.T. Horowitz, Holographic description of AdS cosmologies, JHEP 04 (2005) 005 [hep-th/0503071] [INSPIRE].
N. Turok, B. Craps and T. Hertog, From big crunch to big bang with AdS/CFT, arXiv:0711.1824 [INSPIRE].
B. Craps, T. Hertog and N. Turok, On the Quantum Resolution of Cosmological Singularities using AdS/CFT, Phys. Rev. D 86 (2012) 043513 [arXiv:0712.4180] [INSPIRE].
J. Maldacena, Vacuum decay into Anti de Sitter space, arXiv:1012.0274 [INSPIRE].
J.L.F. Barbon and E. Rabinovici, AdS Crunches, CFT Falls And Cosmological Complementarity, JHEP 04 (2011) 044 [arXiv:1102.3015] [INSPIRE].
J.L.F. Barbon and E. Rabinovici, Conformal Complementarity Maps, JHEP 12 (2013) 023 [arXiv:1308.1921] [INSPIRE].
S.P. Kumar and V. Vaganov, Probing crunching AdS cosmologies, JHEP 02 (2016) 026 [arXiv:1510.03281] [INSPIRE].
S.P. Kumar and V. Vaganov, Quasinormal modes and holographic correlators in a crunching AdS geometry, JHEP 02 (2016) 065 [arXiv:1512.07184] [INSPIRE].
M. Smolkin and N. Turok, Dual description of a 4d cosmology, arXiv:1211.1322 [INSPIRE].
E. Sezgin and P. Sundell, On an exact cosmological solution of higher spin gauge theory, in 4th International Symposium on Quantum Theory and Symmetries and 6th International Workshop on Lie Theory and Its Applications in Physics (QTS-4) (LT-6), Varna, Bulgaria, 15 - 21 August 2005 [hep-th/0511296] [INSPIRE].
E. Sezgin and P. Sundell, An Exact solution of 4 − D higher-spin gauge theory, Nucl. Phys. B 762 (2007) 1 [hep-th/0508158] [INSPIRE].
S.R. Das, J. Michelson, K. Narayan and S.P. Trivedi, Time dependent cosmologies and their duals, Phys. Rev. D 74 (2006) 026002 [hep-th/0602107] [INSPIRE].
A. Awad, S.R. Das, S. Nampuri, K. Narayan and S.P. Trivedi, Gauge Theories with Time Dependent Couplings and their Cosmological Duals, Phys. Rev. D 79 (2009) 046004 [arXiv:0807.1517] [INSPIRE].
R. Auzzi, S. Elitzur, S.B. Gudnason and E. Rabinovici, Time-dependent stabilization in AdS/CFT, JHEP 08 (2012) 035 [arXiv:1206.2902] [INSPIRE].
N. Engelhardt and G.T. Horowitz, Holographic Consequences of a No Transmission Principle, Phys. Rev. D 93 (2016) 026005 [arXiv:1509.07509] [INSPIRE].
A. Bzowski, T. Hertog and M. Schillo, Cosmological singularities encoded in IR boundary correlations, JHEP 05 (2016) 168 [arXiv:1512.05761] [INSPIRE].
N. Engelhardt and A.C. Wall, Extremal Surface Barriers, JHEP 03 (2014) 068 [arXiv:1312.3699] [INSPIRE].
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The Black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].
G. Festuccia and H. Liu, Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I., JHEP 04 (2006) 044 [hep-th/0506202] [INSPIRE].
G. Festuccia and H. Liu, The Arrow of time, black holes, and quantum mixing of large N Yang-Mills theories, JHEP 12 (2007) 027 [hep-th/0611098] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, Cubic Interaction in Extended Theories of Massless Higher Spin Fields, Nucl. Phys. B 291 (1987) 141 [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, in The many faces of the superworld, M.A. Shifman eds., World Scientific, New York U.S.A. (1999) [hep-th/9910096] [INSPIRE].
M. Moshe and J. Zinn-Justin, Quantum field theory in the large N limit: A Review, Phys. Rept. 385 (2003) 69 [hep-th/0306133] [INSPIRE].
J. Zinn-Justin, Quantum field theory and critical phenomena, Int. Ser. Monogr. Phys. 113 (2002) 1 [INSPIRE].
F. Cooper, S. Habib, Y. Kluger, E. Mottola, J.P. Paz and P.R. Anderson, Nonequilibrium quantum fields in the large N expansion, Phys. Rev. D 50 (1994) 2848 [hep-ph/9405352] [INSPIRE].
F. Cooper, S. Habib, Y. Kluger and E. Mottola, Nonequilibrium dynamics of symmetry breaking in lambda Phi**4 field theory, Phys. Rev. D 55 (1997) 6471 [hep-ph/9610345] [INSPIRE].
D. Boyanovsky, H.J. de Vega, R. Holman, D.S. Lee and A. Singh, Dissipation via particle production in scalar field theories, Phys. Rev. D 51 (1995) 4419 [hep-ph/9408214] [INSPIRE].
D. Boyanovsky, D. Cormier, H.J. de Vega and R. Holman, Out-of-equilibrium dynamics of an inflationary phase transition, Phys. Rev. D 55 (1997) 3373 [hep-ph/9610396] [INSPIRE].
D. Boyanovsky, D. Cormier, H.J. de Vega, R. Holman and S.P. Kumar, Nonperturbative quantum dynamics of a new inflation model, Phys. Rev. D 57 (1998) 2166 [hep-ph/9709232] [INSPIRE].
L.F. Abbott and S.R. Coleman, The Collapse of an Anti-de Sitter Bubble, Nucl. Phys. B 259 (1985) 170 [INSPIRE].
S.A. Hartnoll and S.P. Kumar, The O(N ) model on a squashed S 3 and the Klebanov-Polyakov correspondence, JHEP 06 (2005) 012 [hep-th/0503238] [INSPIRE].
N.D. Birrell and P.C.W. Davies, Quantum Fields in Curved Space, Cambridge University Press, Cambridge U.K. (1982).
J.S. Dowker and R. Critchley, Effective Lagrangian and Energy Momentum Tensor in de Sitter Space, Phys. Rev. D 13 (1976) 3224 [INSPIRE].
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Kumar, S.P., Vaganov, V. Nonequilibrium dynamics of the O(N ) model on dS3 and AdS crunches. J. High Energ. Phys. 2018, 92 (2018). https://doi.org/10.1007/JHEP03(2018)092
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DOI: https://doi.org/10.1007/JHEP03(2018)092