2023/12/15 by Weiguang Cao, Cao, Weiguang, Xiaochuan Lu +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions #Representation Theory (math.RT) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2312.10139
openalex publication_date 2023/12/15 · openalex created_date 2023/12/20 · openalex updated_date 2026/07/29
We identify constraints in the energy spectra of quantum theories that have a global O(N) symmetry, where N is treated as a continuous parameter. We point out that a class of evanescent states fall out of the spectrum at integer values of N in pairs, via an annihilation mechanism. This forces the energies of the states in such a pair to approach equality as N approaches a certain integer, with both states disappearing at precisely integer N and the point of would-be degeneracy. These constraints occur between different irreducible representations of the analytic continuation of O(N) and hold non-perturbatively. We give examples in the spectra of the critical O(N) model.