Marginally stable solutions

In previous work constant magnetic field strength solutions for SU(2) gauge theory on a torus were found, which somewhat surprisingly turned out to be classically stable. This was called marginal stability, as moving along one of its zero-modes, two of the stable modes turn unstable. Here we investigate the stability under quantum fluctuations in the domain where the solutions possess the marginal stability at the classical level.Comment: 4p with 2 figs, as one uuencoded PostScript.gz file, presented at Lattice'95, Melbourne, 11-15 July, 199

Instanton Moduli for T**3xR

We review the specific problems that arise when studying instantons on a torus. We discuss how the Nahm transformation shows that no exact charge one instanton on T**4 can exist. However, taking one of the directions (the time) to infinity, it can be shown that vacuum to vacuum tunnelling solutions exist. A precise description of the moduli space for T**3xR, studied numerically using lattice techniques, remains an interesting open problem. New is an explicit application of the Nahm transformation to (anti-)selfdual constant curvature solutions on T**4 and a discussion of its properties relevant to instantons on T**3xR.Comment: 12p with 3 figs, uufiles -gz format. Talk at the 29th Int. Symp. on the Theory of Elem. Part., Buckow, 29 Aug.-2 Sept., 1995

Glueball Spectroscopy on S^3

For SU(2) gauge theory on the three-sphere we implement the influence of the boundary of the fundamental domain, and in particular the $\theta$-dependence, on a subspace of low-energy modes of the gauge field. We construct a basis of functions that respect these boundary conditions and use these in a variational approximation of the spectrum of the lowest order effective hamiltonian.Comment: 8p. latex, 3 uuencoded PostScript figures appende

One-loop effective action for SU(2) gauge theory on S^3

We consider the effective theory for the low-energy modes of SU(2) gauge theory on the three-sphere. By explicitely integrating out the high-energy modes, the one-loop correction to the hamiltonian for this problem is obtained. We calculate the influence of this correction on the glueball spectrum.Comment: 12p. latex, 3 PostScript figures included (epsf

A new approach to instanton calculations in the O(3) nonlinear sigma model

We construct all instantons in the \nlsig\ on a cylindrical space-time, known not to exist on a finite time interval. The scale parameter, $\rho$, is related to the boundary condition in time. This may cure the $\rho\rightarrow0$ divergent instanton gas, through a proper inclusion of in and out states in the path integral.Comment: References added and corrected. Contribution to Lattice'94, 27 Sep - 1 Oct 1994, Bielefeld, Germany. 3 pages PostScript, uuencoded compresse

On Nahm's transformation with twisted boundary conditions

Following two different tracks, we arrive at a definition of Nahm's transformation valid for self-dual fields on the 4-dimensional torus with non-zero twist tensor.The transform is again a self-dual gauge field defined on a new torus and with non-zero twist tensor. It preserves the property of being an involution.Comment: 18 page

Nahm dualities on the torus - a synthesis

We give a unified description of self-dual SU(2) gauge fields on tori of size lt x ls^3 based on a mixture of analytical and numerical methods using the Nahm transformation, extended to the case of twisted boundary conditions. We show how torus calorons (lt/ls small) are Nahm dual to the torus instantons (lt/ls large). Holonomies are dual to the locations of constituents, this duality becoming exact in the limiting cases ls or lt --> infinity. Implications for the moduli spaces are discussed.Comment: Latex, 22 pages, 8 figures in 11 postscript file

One-loop anisotropy for improved actions

We determine the one-loop correction to the anisotropy factor for the square Symanzik improved lattice action, extracted fromthe finite volume effective action for SU(N) gauge theories in the background of a zero-momentum gauge field. The result is smaller by approximately a factor 3 than the one-loop correction for the anisotropic Wilson action. We also comment on the Hamiltonian limit.Comment: 11 pages, 1 figur

Glueballs on the three-sphere

We study the non-perturbative effects of the global features of the configuration space for SU(2) gauge theory on the three-sphere. The strategy is to reduce the full problem to an effective theory for the dynamics of the low-energy modes. By explicitly integrating out the high-energy modes, the one-loop correction to the effective hamiltonian is obtained. Imposing the $\theta$ dependence through boundary conditions in configuration space incorporates the non-perturbative effects of the non-contractable loops in the full configuration space. After this we obtain the glueball spectrum of the effective theory with a variational method.Comment: 48 p LaTeX, 13 Postscript figures appende

Multi-Caloron solutions

We discuss the construction of multi-caloron solutions with non-trivial holonomy, both as approximate superpositions and exact self-dual solutions. The charge k SU(n) moduli space can be described by kn constituent monopoles. Exact solutions help us to understand how these constituents can be seen as independent objects, which seems not possible with the approximate superposition. An "impurity scattering" calculation provides relatively simple expressions. Like at zero temperature an explicit parametrization requires solving a quadratic ADHM constraint, achieved here for a class of axially symmetric solutions. We will discuss the properties of these exact solutions in detail, but also demonstrate that interesting results can be obtained without explicitly solving for the constraint.Comment: 31 pages, 7 figures (in 19 parts