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タイトル: | Flow equation for the scalar model in the large $N$ expansion and its applications |
著者: | Aoki, Sinya Balog, Janos Onogi, Tetsuya Weisz, Peter |
著者名の別形: | 青木, 愼也 |
キーワード: | B32 Renormalization and renormalization group equation B34 Field theories in lower dimensions B35 Solitons, monopoles and instantons, 1/N expansion |
発行日: | Apr-2017 |
出版者: | Oxford University Press (OUP) |
誌名: | Progress of Theoretical and Experimental Physics |
巻: | 2017 |
号: | 4 |
論文番号: | 043B01 |
抄録: | We study the flow equation of the O(N) φ4 model in d dimensions at the next-to-leading order (NLO) in the 1/N expansion. Using the Schwinger–Dyson equation, we derive 2-pt and 4-pt functions of flowed fields. As the first application of the NLO calculations, we study the running coupling defined from the connected 4-pt function of flowed fields in d+1-dimensional theory. We show in particular that this running coupling has not only an ultraviolet fixed point but also an infrared fixed point (Wilson–Fisher fixed point) in 3-dimensional massless scalar theory. As the second application, we calculate the NLO correction to the induced metric in d+1 dimensions with d=3 in the massless limit. While the induced metric describes a 4-dimensional Euclidean Anti-de-Sitter (AdS) space at the leading order, as shown in the previous paper, the NLO corrections make the space asymptotically AdS only in the UV and IR limits. Remarkably, while the AdS radius does not receive an NLO correction in the UV limit, the AdS radius decreases at the NLO in the IR limit, which corresponds to the Wilson–Fisher fixed point in the original scalar model in 3 dimensions. |
著作権等: | © The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Funded by SCOAP3. |
URI: | http://hdl.handle.net/2433/250309 |
DOI(出版社版): | 10.1093/ptep/ptx025 |
出現コレクション: | 学術雑誌掲載論文等 |
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