Magnetic Monopole Content of Hot Instantons

Although many qualitative features of QCD are well described by a vacuum state dominated by an instanton “liquid’, confinement appears to be an exception [1]. Instead, magnetic monopoles are thought to be the crucial ingredient. This raises the question of how magnetic degrees of freedom can be incorporated into (or reconciled with) an instanton “liquid”. A recent step in this direction was taken by Brower, Orginos and Tan (BOT)[2] who studied in detail the magnetic content of a single isolated instanton, defining magnetic currents via the Maximally Abelian (MA) projection. They found a marginally stable direction for the formation of a monopole loop. Now with the more general caloron solution of T. Kraan and P. van Baal [3], and K. Lee and C. Lu [4], this analysis can be extended to an isolated SU(2) instanton at finite temperature (T ) with a non-trivial holonomy (ω) for the Polyakov loop. The resultant picture that emerges is appealing (see Fig. 1). For ω = 0, the small monopole loop at the core of a cold instanton grows in size as one increases the temperature and is transformed into a single static ’t Hooft-Polyakov monopole at infinite temperature, as noted earlier by Rossi [5]. Note that the other quadrants of Fig. 1 can be