\(p\)-adic CFT is a holographic tensor network
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Publication:2421708
DOI10.1007/JHEP04(2019)170zbMATH Open1415.81082arXiv1902.01411OpenAlexW2911516310WikidataQ127953885 ScholiaQ127953885MaRDI QIDQ2421708
Author name not available (Why is that?)
Publication date: 17 June 2019
Published in: (Search for Journal in Brave)
Abstract: The p-adic AdS/CFT correspondence relates a CFT living on the p-adic numbers to a system living on the Bruhat-Tits tree. Modifying our earlier proposal for a tensor network realization of p-adic AdS/CFT, we prove that the path integral of a p-adic CFT is equivalent to a tensor network on the Bruhat-Tits tree, in the sense that the tensor network reproduces all correlation functions of the p-adic CFT. Our rules give an explicit tensor network for any p-adic CFT (as axiomatized by Melzer), and can be applied not only to the p-adic plane, but also to compute any correlation functions on higher genus p-adic curves. Finally, we apply them to define and study RG flows in p-adic CFTs, establishing in particular that any IR fixed point is itself a p-adic CFT.
Full work available at URL: https://arxiv.org/abs/1902.01411
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