Abstract
In this paper, we compute the effective action of both a scalar field and a Dirac spinor field in the global de Sitter space of any dimension d using the in-/out-state formalism. We show that there is particle production in even dimensions for both scalar field and spinor field. The in-out vacuum amplitude \( {\mathcal{Z}}_{\mathrm{in}/\mathrm{out}} \) is divergent at late times. By using dimensional regularization, we extract the finite part of log \( {\mathcal{Z}}_{\mathrm{in}/\mathrm{out}} \) for d even and the logarithmically divergent part of log \( {\mathcal{Z}}_{\mathrm{in}/\mathrm{out}} \) for d odd. We also find that the regularized in-out vacuum amplitude equals the ratio of determinants associated with different quantizations in AdSd upon the identification of certain parameters in the two theories.
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References
P. Candelas and D.J. Raine, General Relativistic Quantum Field Theory-An Exactly Soluble Model, Phys. Rev. D 12 (1975) 965 [INSPIRE].
J.S. Dowker and R. Critchley, Scalar Effective Lagrangian in de Sitter Space, Phys. Rev. D 13 (1976) 224 [INSPIRE].
E. Mottola, Particle Creation in de Sitter Space, Phys. Rev. D 31 (1985) 754 [INSPIRE].
B. Allen, Vacuum States in de Sitter Space, Phys. Rev. D 32 (1985) 3136 [INSPIRE].
R. Bousso, A. Maloney and A. Strominger, Conformal vacua and entropy in de Sitter space, Phys. Rev. D 65 (2002) 104039 [hep-th/0112218] [INSPIRE].
M. Fukuma, S. Sugishita and Y. Sakatani, Propagators in de Sitter space, Phys. Rev. D 88 (2013) 024041 [arXiv:1301.7352] [INSPIRE].
E. Joung, J. Mourad and R. Parentani, Group theoretical approach to quantum fields in de Sitter space. I. The Principle series, JHEP 08 (2006) 082 [hep-th/0606119] [INSPIRE].
E.T. Akhmedov, K.V. Bazarov, D.V. Diakonov, U. Moschella, F.K. Popov and C. Schubert, Propagators and Gaussian effective actions in various patches of de Sitter space, Phys. Rev. D 100 (2019) 105011 [arXiv:1905.09344] [INSPIRE].
A.M. Polyakov, de Sitter space and eternity, Nucl. Phys. B 797 (2008) 199 [arXiv:0709.2899] [INSPIRE].
S.P. Kim, Vacuum Structure of de Sitter Space, arXiv:1008.0577 [INSPIRE].
P.R. Anderson and E. Mottola, Instability of global de Sitter space to particle creation, Phys. Rev. D 89 (2014) 104038 [arXiv:1310.0030] [INSPIRE].
S.S. Gubser and I. Mitra, Double trace operators and one loop vacuum energy in AdS/CFT, Phys. Rev. D 67 (2003) 064018 [hep-th/0210093] [INSPIRE].
S.S. Gubser and I.R. Klebanov, A Universal result on central charges in the presence of double trace deformations, Nucl. Phys. B 656 (2003) 23 [hep-th/0212138] [INSPIRE].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].
A. Allais, Double-trace deformations, holography and the c-conjecture, JHEP 11 (2010) 040 [arXiv:1007.2047] [INSPIRE].
R. Aros and D.E. Diaz, Determinant and Weyl anomaly of Dirac operator: a holographic derivation, J. Phys. A 45 (2012) 125401 [arXiv:1111.1463] [INSPIRE].
B.S. DeWitt, Quantum Field Theory in Curved Space-Time, Phys. Rept. 19 (1975) 295 [INSPIRE].
A.I. Nikishov, On vacuum-vacuum amplitude and Bogolyubov coefficients, J. Exp. Theor. Phys. 96 (2003) 180 [hep-th/0207085] [INSPIRE].
S.P. Kim, H.K. Lee and Y. Yoon, Effective Action of Scalar QED in Electric Field Backgrounds, Phys. Rev. D 78 (2008) 105013 [arXiv:0807.2696] [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
F.W.J. Olver et al., NIST Digital Library of Mathematical Functions, Release 1.0.25 of 2019-12-15, http://dlmf.nist.gov/.
R. Camporesi and A. Higuchi, On the Eigen functions of the Dirac operator on spheres and real hyperbolic spaces, J. Geom. Phys. 20 (1996) 1 [gr-qc/9505009] [INSPIRE].
I.S. Gradshtein, I.M. Ryzhik, D. Zwillinger and V.H. Moll, Table of integrals, series, and products, Academic Press (2015).
E.T. Akhmedov, Real or Imaginary? (On pair creation in de Sitter space), Mod. Phys. Lett. A 25 (2010) 2815 [arXiv:0909.3722] [INSPIRE].
S. Deser and A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047] [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
P.O. Mazur and E. Mottola, Weyl cohomology and the effective action for conformal anomalies, Phys. Rev. D 64 (2001) 104022 [hep-th/0106151] [INSPIRE].
S. Nojiri and S.D. Odintsov, Conformal anomaly from dS/CFT correspondence, Phys. Lett. B 519 (2001) 145 [hep-th/0106191] [INSPIRE].
R. Aros, D.E. Diaz and A. Montecinos, A Note on a gauge-gravity relation and functional determinants, J. Phys. A 43 (2010) 295401 [arXiv:1004.1394] [INSPIRE].
D. Das, S.R. Das and G. Mandal, Double Trace Flows and Holographic RG in dS/CFT correspondence, JHEP 11 (2013) 186 [arXiv:1306.0336] [INSPIRE].
A. Monin, Partition function on spheres: How to use zeta function regularization, Phys. Rev. D 94 (2016) 085013 [arXiv:1607.06493] [INSPIRE].
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Jiang, J. Scalar and spinor effective actions in global de Sitter. J. High Energ. Phys. 2020, 37 (2020). https://doi.org/10.1007/JHEP06(2020)037
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DOI: https://doi.org/10.1007/JHEP06(2020)037