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SIGMA 5 (2009), 047, 14 pages arXiv:0812.0176
https://doi.org/10.3842/SIGMA.2009.047
Contribution to the Proceedings of the VIIth Workshop ''Quantum Physics with Non-Hermitian Operators''
PT Symmetry and QCD: Finite Temperature and Density
Michael C. Ogilvie and Peter N. Meisinger
Department of Physics, Washington University, St. Louis, MO 63130, USA
Received November 15, 2008, in final form April 10, 2009; Published online April 17, 2009
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 μ, 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.
Key words:
PT symmetry; QCD.
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