Abstract
We consider the semi-classical expansion of the Bunch-Davies wavefunction with future boundary condition in position space for a real scalar field, conformally coupled to a classical de Sitter background in the expanding Poincaré patch with quartic selfinteraction. In the future boundary limit the wave function takes the form of the generating functional of a Euclidean conformal field theory for which we calculate the anomalous dimensions of the double trace deformations at one loop order using results obtained from Euclidean Anti de Sitter space. We find analytic expressions for some subleading twist operators and an algorithm to obtain expressions for general twist.
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References
V. F. Mukhanov and G. V. Chibisov, Quantum Fluctuations and a Nonsingular Universe, JETP Lett. 33 (1981) 532 [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, in Strings 2001: International Conference, 6, 2001, hep-th/0106109 [INSPIRE].
J. M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
D. Anninos, T. Anous, D. Z. Freedman and G. Konstantinidis, Late-time Structure of the Bunch-Davies de Sitter Wavefunction, JCAP 11 (2015) 048 [arXiv:1406.5490] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, Class. Quant. Grav. 34 (2017) 015009 [arXiv:1108.5735] [INSPIRE].
G. S. Ng and A. Strominger, State/Operator Correspondence in Higher-Spin dS/CFT, Class. Quant. Grav. 30 (2013) 104002 [arXiv:1204.1057] [INSPIRE].
D. Anninos, F. Denef, G. Konstantinidis and E. Shaghoulian, Higher Spin de Sitter Holography from Functional Determinants, JHEP 02 (2014) 007 [arXiv:1305.6321] [INSPIRE].
D. Anninos, F. Denef, R. Monten and Z. Sun, Higher Spin de Sitter Hilbert Space, JHEP 10 (2019) 071 [arXiv:1711.10037] [INSPIRE].
C. Sleight and M. Taronna, Bootstrapping Inflationary Correlators in Mellin Space, JHEP 02 (2020) 098 [arXiv:1907.01143] [INSPIRE].
G. Konstantinidis, R. Mahajan and E. Shaghoulian, Late-time Structure of the Bunch-Davies FRW Wavefunction, JHEP 10 (2016) 103 [arXiv:1608.06163] [INSPIRE].
A. Strominger, Inflation and the dS/CFT correspondence, JHEP 11 (2001) 049 [hep-th/0110087] [INSPIRE].
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization, arXiv:2005.04234 [INSPIRE].
V. Gorbenko and L. Senatore, λϕ4 in dS, arXiv:1911.00022 [INSPIRE].
I. Bertan, I. Sachs and E. D. Skvortsov, Quantum ϕ4 Theory in AdS4 and its CFT Dual, JHEP 02 (2019) 099 [arXiv:1810.00907] [INSPIRE].
I. Bertan and I. Sachs, Loops in Anti-de Sitter Space, Phys. Rev. Lett. 121 (2018) 101601 [arXiv:1804.01880] [INSPIRE].
B. Allen, Vacuum States in de Sitter Space, Phys. Rev. D 32 (1985) 3136 [INSPIRE].
M. Fukuma, S. Sugishita and Y. Sakatani, Propagators in de Sitter space, Phys. Rev. D 88 (2013) 024041 [arXiv:1301.7352] [INSPIRE].
E. T. Akhmedov, Lecture notes on interacting quantum fields in de Sitter space, Int. J. Mod. Phys. D 23 (2014) 1430001 [arXiv:1309.2557] [INSPIRE].
N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics. Cambridge Univ. Press, Cambridge, UK, 2, 1984, 10.1017/CBO9780511622632 [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].
J. Hartle and S. Hawking, Wave Function of the Universe, Adv. Ser. Astrophys. Cosmol. 3 (1987) 174.
W. Mueck and K. S. Viswanathan, Conformal field theory correlators from classical scalar field theory on AdS(d+1), Phys. Rev. D 58 (1998) 041901 [hep-th/9804035] [INSPIRE].
S. Rychkov, EPFL Lectures on Conformal Field Theory in D >= 3 Dimensions, SpringerBriefs in Physics. 1, 2016, https://doi.org/10.1007/978-3-319-43626-5 [arXiv:1601.05000] [INSPIRE].
A. L. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].
F. A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].
A. L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective Conformal Theory and the Flat-Space Limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].
B. Basso and G. P. Korchemsky, Anomalous dimensions of high-spin operators beyond the leading order, Nucl. Phys. B 775 (2007) 1 [hep-th/0612247] [INSPIRE].
A. L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The Analytic Bootstrap and AdS Superhorizon Locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].
L. F. Alday, A. Bissi and T. Lukowski, Large spin systematics in CFT, JHEP 11 (2015) 101 [arXiv:1502.07707] [INSPIRE].
K. Symanzik, On Calculations in conformal invariant field theories, Lett. Nuovo Cim. 3 (1972) 734 [INSPIRE].
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Heckelbacher, T., Sachs, I. Loops in dS/CFT. J. High Energ. Phys. 2021, 151 (2021). https://doi.org/10.1007/JHEP02(2021)151
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DOI: https://doi.org/10.1007/JHEP02(2021)151