2008/12/31 by Michael C. Ogilvie, Peter N. Meisinger · 7 citations
Physics and Astronomy · #Chiral symmetry breaking #Gauge theory #Hamiltonian (control theory) #Lattice field theory #Lattice gauge theory #Magnetic monopole #Mathematical physics #Neutrino Physics Research #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Quark #Theoretical physics #hep-th
paper · pdf · doi:10.3842/sigma.2009.047
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine) · 10 figures; invited talk at PHHQP VII, Benasque 2008
arxiv created 2009/04/17 · openalex publication_date 2009/04/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The relevance of PT symmetry to quantum chromodynamics (QCD), the gauge theory of the strong interactions, is explored in the context of finite temperature and density. Two significant problems in QCD are studied: the sign problem of finite-density QCD, and the problem of confinement. It is proven that the effective action for heavy quarks at finite density is PT -symmetric. For the case of 1 + 1 dimensions, the PT -symmetric Hamiltonian, although not Hermitian, has real eigenvalues for a range of values of the chemical potential , solving the sign problem for this model. The effective action for heavy quarks is part of a potentially large class of generalized sine-Gordon models which are non-Hermitian but are PT -symmetric. Generalized sine-Gordon models also occur naturally in gauge theories in which magnetic monopoles lead to confinement. We explore gauge theories where monopoles cause confinement at arbitrarily high temperatures. Several different classes of monopole gases exist, with each class leading to different string tension scaling laws. For one class of monopole gas models, the PT -symmetric affine Toda field theory emerges naturally as the effective theory. This in turn leads to sine-law scaling for string tensions, a behavior consistent with lattice simulations.