Abstract
We continue the series of articles on the application of Landau-Ginzburg mean-field theory to unveil the basic phase structure of tensorial field theories which are characterized by combinatorially non-local interactions. Among others, this class covers tensor field theories (TFT) which lead to a new class of conformal field theories highly relevant for investigations on the AdS/CFT conjecture. Moreover, it also encompasses models within the tensorial group field theory (TGFT) approach to quantum gravity. Crucially, in the infrared we find that the effective mass of the modes relevant for the critical behavior vanishes not only at criticality but also throughout the entire phase of non-vanishing vacuum expectation value due to the non-locality of the interactions. As a consequence, one encounters there the emergence of scale invariance on configuration space which is potentially enhanced to conformal invariance thereon.
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Acknowledgments
The authors thank J. Ben Achour, L. Marchetti, R. Schmieden, and J. Thürigen for insightful discussions. DO acknowledges financial support from the ATRAE programme of the Spanish Government, through the grant PR28/23 ATR2023-145735. DO and AGAP acknowledge funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) research grants OR432/3-1 and OR432/4-1 and the John-Templeton Foundation via research grant 6242. AFJ acknowledges support by the DFG under Grant No. 406116891 within the Research Training Group RTG 2522/1 and under Grant No. 422809950. RD, AFJ, and AGAP are grateful for the generous financial support by the MCQST via the seed funding Aost 862933-9 granted to AGAP and the seed funding Aost 862981-8 granted to Jibril Ben Achour by the DFG under Germany’s Excellence Strategy — EXC-2111 — 390814868. AGAP in particular acknowledges funding by the DFG under the author’s project number 527121685 as a Principal Investigator.
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Dekhil, R., Jercher, A.F., Oriti, D. et al. Scale invariance beyond criticality within the mean-field analysis of tensorial field theories. J. High Energ. Phys. 2024, 50 (2024). https://doi.org/10.1007/JHEP08(2024)050
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DOI: https://doi.org/10.1007/JHEP08(2024)050