\(O(N)\) model in Euclidean de Sitter space: beyond the leading infrared approximation
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Publication:1636196
DOI10.1007/JHEP09(2016)117zbMATH Open1390.83470arXiv1606.03481MaRDI QIDQ1636196
Author name not available (Why is that?)
Publication date: 12 June 2018
Published in: (Search for Journal in Brave)
Abstract: We consider an scalar field model with quartic interaction in -dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling constant and in 1/N. We explicitly perform the calculation up to the next-to-next-to-leading order in and up to next-to-leading order in 1/N. The results reduce to those known in the leading infrared approximation. We also show that they coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large N limit, provided the same renormalization scheme is used.
Full work available at URL: https://arxiv.org/abs/1606.03481
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