Monopole Constituents inside SU(n) Calorons

We present a simple result for the action density of the SU(n) charge one periodic instantons - or calorons - with arbitrary non-trivial Polyakov loop P_oo at spatial infinity. It is shown explicitly that there are n lumps inside the caloron, each of which represents a BPS monopole, their masses being related to the eigenvalues of P_oo. A suitable combination of the ADHM construction and the Nahm transformation is used to obtain this result.Comment: 8 pages, 1 figure (in three parts), late

Instantons, Monopoles and Toric HyperKaehler Manifolds

In this paper, the metric on the moduli space of the k=1 SU(n) periodic instanton -or caloron- with arbitrary gauge holonomy at spatial infinity is explicitly constructed. The metric is toric hyperKaehler and of the form conjectured by Lee and Yi. The torus coordinates describe the residual U(1)^{n-1} gauge invariance and the temporal position of the caloron and can also be viewed as the phases of n monopoles that constitute the caloron. The (1,1,..,1) monopole is obtained as a limit of the caloron. The calculation is performed on the space of Nahm data, which is justified by proving the isometric property of the Nahm construction for the cases considered. An alternative construction using the hyperKaehler quotient is also presented. The effect of massless monopoles is briefly discussed.Comment: 30 pages, latex2

New Instanton Solutions at Finite Temperature

We discuss the newly found exact instanton solutions at finite temperature with a non-trivial Polyakov loop at infinity. They can be described in terms of monopole constituents and we discuss in this context an old result due to Taubes how to make out of monopoles non-trivial topological charge configurations, with possible applications to abelian projection.Comment: 6 pages, 2 figures (in 5 parts), latex using espcrc1.sty, presented at "QCD at Finite Baryon Density", April 27-30, 1998, Bielefeld, German

Gluino Condensation in an Interacting Instanton Ensemble

We perform a semi-classical study of chiral symmetry breaking and of the spectrum of the Dirac operator in QCD with adjoint fermions. For this purpose we calculate matrix elements of the adjoint Dirac operator between instanton zero modes and study their symmetry properties. We present simulations of the instanton ensemble for different numbers of Majorana fermions in the adjoint representation. These simulations provide evidence that instantons lead to gluino condensation in supersymmetric gluodynamics.Comment: 32 pages, 5 figures, acknowledgment adde

Continuity, Deconfinement, and (Super) Yang-Mills Theory

We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl fermion on R^3xS^1 as a function of the fermion mass m and the compactification scale L. This theory reduces to thermal pure gauge theory as m->infinity and to circle-compactified (non-thermal) supersymmetric gluodynamics in the limit m->0. In the m-L plane, there is a line of center symmetry changing phase transitions. In the limit m->infinity, this transition takes place at L_c=1/T_c, where T_c is the critical temperature of the deconfinement transition in pure Yang-Mills theory. We show that near m=0, the critical compactification scale L_c can be computed using semi-classical methods and that the transition is of second order. This suggests that the deconfining phase transition in pure Yang-Mills theory is continuously connected to a transition that can be studied at weak coupling. The center symmetry changing phase transition arises from the competition of perturbative contributions and monopole-instantons that destabilize the center, and topological molecules (neutral bions) that stabilize the center. The contribution of molecules can be computed using supersymmetry in the limit m=0, and via the Bogomolnyi--Zinn-Justin (BZJ) prescription in the non-supersymmetric gauge theory. Finally, we also give a detailed discussion of an issue that has not received proper attention in the context of N=1 theories---the non-cancellation of nonzero-mode determinants around supersymmetric BPS and KK monopole-instanton backgrounds on R^3xS^1. We explain why the non-cancellation is required for consistency with holomorphy and supersymmetry and perform an explicit calculation of the one-loop determinant ratio.Comment: A discussion of the non-cancellation of the nonzero mode determinants around supersymmetric monopole-instantons in N=1 SYM on R^3xS^1 is added, including an explicit calculation. The non-cancellation is, in fact, required by supersymmetry and holomorphy in order for the affine-Toda superpotential to be reproduced. References have also been adde