Fluctuations in the non-linear supersymmetric hyperbolic sigma model with long-range interactions

Abstract

We consider a class of non-linear supersymmetric hyperbolic sigma models with long-range interactions on boxes in ${\mathbb{Z}}^d$ and on a hierarchical lattice. We prove that the random field associated to a marginal in horospherical coordinates has asymptotically arbitrarily small fluctuations for large enough interactions, uniformly in the size of the boxes. This can be viewed as a strong version of spontaneous breaking of the Lorentz boost symmetry.

27 pages, 2 figures. This manuscripts was obtained by splitting and updating arXiv:2305.07359v1 into this manuscript and arXiv:2305.07359v2