Constraints on the Dirac spectrum from chiral symmetry restoration and the fate of U(1)_A symmetry

2024/12/03 by Matteo Giordano, Giordano, Matteo
Physics and Astronomy · #Black Holes and Theoretical Physics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2412.02517

openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I discuss chiral symmetry restoration in the chiral limit m→ 0 of QCD with two light quark flavours of mass m, focussing on its consequences for scalar and pseudoscalar susceptibilities, and on the resulting constraints on the Dirac spectrum. I show that U(1)_A symmetry remains broken in the SU(2)_A symmetric phase if the spectral density ρ(λ;m) develops a singular near-zero peak, tending to O(m⁴)/λ in the chiral limit. Moreover, SU(2)_A restoration requires that the number of modes in the peak be proportional to the topological susceptibility, indicating that such a peak must be of topological origin.

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