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Résumé |
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. In this talk I will describe constraints obtained using the non-perturbative conformal bootstrap in theories with hypercubic and hypertetrahedral symmetry in d=3 spacetime dimensions. Comparisons will be drawn with previous perturbative studies of these theories, performed using the \epsilon=4-d expansion starting from Lagrangians involving N scalar fields. The N=3 cubic theory is relevant for statistical physics, particularly cubic magnets at criticality and structural phase transitions. The old question of whether cubic magnets, like Fe or Ni, are described at criticality by the Heisenberg or cubic universality class will be extensively discussed. For the hypertetrahedral theory evidence will be presented of a non-conformal window in N, as suggested in perturbation theory by the \epsilon expansion. (Based on arXiv:1801.07127.) |
