QCD and instantons at finite temperature

David J. Gross, Robert D. Pisarski, and Laurence G. Yaffe
Rev. Mod. Phys. 53, 43 – Published 1 January 1981
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Abstract

The current understanding of the behavior of quantum chromodynamics at finite temperature is presented. Perturbative methods are used to explore the high-temperature dynamics. At sufficiently high temperatures the plasma of thermal excitations screens all color electric fields and quarks are unconfined. It is believed that the high-temperature theory develops a dynamical mass gap. However in perturbation theory the infrared behavior of magnetic fluctuations is so singular that beyond some order the perturbative expansion breaks down. The topological classification of finite-energy, periodic fields is presented and the classical solutions which minimize the action in each topological sector are examined. These include periodic instantons and magnetic monopoles. At sufficiently high temperature only fields with integral topological charge can contribute to the functional integral. Electric screening completely suppresses the contribution of fields with nonintegral topological charge. Consequently the θ dependence of the free energy at high temperature is dominated by the contribution of instantons. The complete temperature dependence of the instanton density is explicitly computed and large-scale instantons are found to be suppressed. Therefore the effects of instantons may be reliably calculated at sufficiently high temperature. The behavior of the theory in the vicinity of the transition from the high-temperature quark phase to the low-temperature hadronic phase cannot be accurately computed. However, at least in the absence of light quarks, semiclassical techniques and lattice methods may be combined to yield a simple picture of the dynamics valid for both high and low temperature, and to estimate the transition temperature.

    DOI:https://doi.org/10.1103/RevModPhys.53.43

    ©1981 American Physical Society

    Authors & Affiliations

    David J. Gross

    • Department of Physics, Princeton University, Princeton, New Jersey 08544

    Robert D. Pisarski

    • J. W. Gibbs Laboratories, Yale University, New Haven, Connecticut 06520

    Laurence G. Yaffe*

    • Department of Physics, Princeton University, Princeton, New Jersey 08544

    • *Current address: 452-48, Department of Physics, California Institute of Technology, Pasadena, California 91125.

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    Vol. 53, Iss. 1 — January - March 1981

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