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arXiv · 2408.08136

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

Margherita Disertori·Franz Merkl·Silke W. W. Rolles
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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.

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Margherita Disertori, Franz Merkl, Silke W. W. Rolles. 2024-08-15. Fluctuations in the non-linear supersymmetric hyperbolic sigma model with long-range interactions. https://arxiv.org/abs/2408.08136

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