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

2024/08/15 by Margherita Disertori, Disertori, Margherita, Franz Merkl +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 82B20 #Probability (math.PR) #Quantum Chromodynamics and Particle Interactions #secondary 60G60

paper · pdf · doi:10.48550/arxiv.2408.08136

openalex publication_date 2024/08/15 · openalex created_date 2025/01/03 · openalex updated_date 2026/07/28

Abstract

We consider a class of non-linear supersymmetric hyperbolic sigma models with long-range interactions on boxes in 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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