Monopoles and vortices in Yang-Mills plasma
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ELEMENTARY PARTICLES AND FIELDS Theory
Monopoles and Vortices in Yang–Mills Plasma* M. N. Chernodub1), 2)** and V. I. Zakharov2), 3) Received October 24, 2008; in final form, May 12, 2009
Abstract—We discuss the role of magnetic degrees of freedom in Yang–Mills plasma at temperatures above and of order of the critical temperature Tc . While at zero temperature the magnetic degrees of freedom are condensed and electric degrees of freedom are confined, at the point of the phase transition both magnetic and electric degrees of freedom are released into the thermal vacuum. This phenomenon might explain the observed unusual properties of the plasma. PACS numbers: 12.38.Aw, 25.75.Nq, 11.15.Tk DOI: 10.1134/S106377880912014X
1. INTRODUCTION At vanishing temperature, the Yang–Mills theories exhibit the phenomenon of the color confinement. In case of pure Yang–Mills theories, on which we concentrate below, the criterion of the confinement is the area law for large enough Wilson loops: W (C) ∼ exp (−σ · Amin ) or VQQ ¯ (R) → σ · R.
(1)
Here, C is the rectangular contour with time and space dimensions T and R, respectively, Amin ≡ R · T is the minimal area of a surface spanned on the contour C, σ = 0 is the confining string tension, and VQQ ¯ (R) is the heavy-quark potential at large distances R between quark and antiquark. While there is yet no understanding of the confinement from the first principles in the non-Abelian case, it can be modeled in Abelian theories. In particular, in ordinary superconductor the potential between external magnetic monopoles grows linearly at large distances R, ∼ σM · R, VMM ¯ mimicking the heavy-quark potential (1). The microscopical mechanism behind this example is the condensation of the Cooper pairs. In the effectivetheory language the mechanism is a condensation of the electrically charged scalar field: φel = 0. ∗
The text was submitted by the authors in English. 1) ´ eration ´ LMPT, CNRS UMR 6083, Fed Denis Poisson, Universite´ de Tours, France. 2) ITEP, Moscow, Russia. 3) INFN, Sezione di Pisa, Italy. ** E-mail: [email protected]
By analogy with this well understood case it was speculated long time ago [1] that in the non-Abelian theories it is the condensate of magnetically charged field, (2) φmagn = 0, that ensures confinement of color charges (1). Within this general framework of the dualsuperconductor model (2) the main question is: what is the microscopical mechanism behind (2). In other words, the question is what is a Yang–Mills analog of the Cooper pairs of the ordinary superconductor? (Remember that we are considering pure Yang–Mills theories without fundamental scalar fields.) A clue to the answer to this question might be provided by the example of the so-called compact U (1) theory [2] where the magnetic degrees of freedom are identified as topological excitations of the original theory. In more detail, the Lagrangian is the same as for a free electromagnetic field: 1 2 , LU (1) = 2 Fμν 4e supplemented, however, by the condition that the Dirac string carries
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