Bootstrapping hypercubic and hypertetrahedral theories in three dimensions

DOI10.1007/JHEP05(2018)035zbMATH Open1391.81174arXiv1801.07127WikidataQ64863135 ScholiaQ64863135MaRDI QIDQ1651079

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Publication date: 11 July 2018

Published in: (Search for Journal in Brave)

Abstract: There are three generalizations of the Platonic solids that exist in all dimensions, namely the hypertetrahedron, the hypercube, and the hyperoctahedron, with the latter two being dual. Conformal field theories with the associated symmetry groups as global symmetries can be argued to exist in $d=3$ spacetime dimensions if the $varepsilon=4-d$ expansion is valid when $varepsilono1$. In this paper hypercubic and hypertetrahedral theories are studied with the non-perturbative numerical conformal bootstrap. In the $N=3$ cubic case it is found that a bound with a kink is saturated by a solution with properties that cannot be reconciled with the $varepsilon$ expansion of the cubic theory. Possible implications for cubic magnets and structural phase transitions are discussed. For the hypertetrahedral theory evidence is found that the non-conformal window that is seen with the $varepsilon$ expansion exists in $d=3$ as well, and a rough estimate of its extent is given.

Full work available at URL: https://arxiv.org/abs/1801.07127

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