Observables in inhomogeneous ground states at large global charge

• Published in: The journal of high energy physics Vol. 2021; no. 8; pp. 1 - 24
• Main Authors: Hellerman, Simeon, Kobayashi, Nozomu, Maeda, Shunsuke, Watanabe, Masataka
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2021; Springer Nature B.V; SpringerOpen
• Subjects: Charge density; Classical and Quantum Gravitation; Configurations; Conformal Field Theory; Dimensional analysis; Effective Field Theories; Elementary Particles; Ground state; High energy physics; Inhomogeneity; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Renormalization Group; String Theory; Toruses; Effective Field Theories; Conformal Field Theory; Renormalization Group
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2021)079

A bstract As a sequel to previous work, we extend the study of the ground state configuration of the D = 3, Wilson-Fisher conformal O (4) model. In this work, we prove that for generic ratios of two charge densities, ρ 1 / ρ 2 , the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for ρ 1 / ρ 2 ≪ 1. We also compute, at fixed set of charges, ρ 1 , ρ 2 , the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale ( ρ 1 + ρ 2 ) 3/2 , as dictated by dimensional analysis and similarly to the case of the O (2) model. Unlike the case of the O (2) model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.