PT Symmetry and QCD: Finite Temperature and Density

Abstract

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 $\mu$, 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.

10 figures; invited talk at PHHQP VII, Benasque 2008

References in corpus (19)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Color superconductivity in dense quark matter
• Introduction to PT-Symmetric Quantum Theory
• SU(2) Calorons and Magnetic Monopoles
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Monopole Constituents inside SU(n) Calorons
• Gluino Condensate and Magnetic Monopoles in Supersymmetric Gluodynamics
• Glueballs and k-strings in SU(N) gauge theories : calculations with improved operators
• Quantum Solitons in Affine Toda Field Theories
• Phenomenological Equations of State for the Quark-Gluon Plasma
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Symmetries and spectrum of SU(2) Lattice Gauge Theory at finite chemical potential
• Two-colour QCD at non-zero quark-number density
• Dual PT-Symmetric Quantum Field Theories
• Instantons and Magnetic Monopoles on $R^3\times S^1$ with Arbitrary Simple Gauge Groups
• Confining ensemble of dyons
• New Phases of SU(3) and SU(4) at Finite Temperature
• Complete High Temperature Expansions for One-Loop Finite Temperature Effects
• Exotic phases of finite temperature SU(N) gauge theories with massive fermions: F, Adj, A/S

Cited by in corpus (5)

• Finite Volume Phases of Large N Gauge Theories with Massive Adjoint Fermions
• PT Symmetry in Classical and Quantum Statistical Mechanics
• Complex spectrum of finite-density lattice QCD with static quarks at strong coupling
• The sign problem and Abelian lattice duality
• Complex spectrum of spin models for finite-density QCD