Exact Caloron solutions with non-trivial holonomy

Here we make available the C-programmes that can be used for making plots of the energy density ((SU(2) and SU(3)) and the trace of the Polyakov loop and the zero-mode density (SU(2) only). The output (Profile[b]) is in a format that easily allows one to plot it using the Mathematica command ListPlot3D[Profile[b]].

A number of these programmes were used to compare lattice and analytic results as discussed in the paper:

The analytic results are based on the papers by T.C. Kraan and P. van Baal, A short summary of the analytic results can be found in

Warning: avoid being exactly at the location of a constituent monopole or for t=0 at "the center of mass" (gauge singularity) to avoid numerical instabilities.

Available are the following modules:

These modules are called in the C-programmes: To run the C-programmes on a UNIX platform use:
The analytic result for the SU(2) fermion zero-mode density is based on the paper: The following module was added to the existing ones: This module is called in the SU(2) C-programmes (beware when your file system is case insensitive): These are to be used exactly as (and make obsolete) the earlier SU(2) programmes, replacing su2 by SU2 everywhere (use the same makefile to compile these programmes: make SU2 SU2-t-z SU2-r-z SU2-lat). The only change is that now also the fermion zero-mode density is given (Profile[0]=action density, Nzmsq(X) or Profile[-1]=anti-periodic zero-mode density, Profile[-2]=periodic zero-mode density).
For convenience one can download all C-programmes through the uufiles c.uu.
Disclaimer: Users themselves are responsible for the validity of the results obtained with these programmes.

Results for SU(N>2) zero-modes (see a movie with changing boundary conditions for SU(3)) can be found in :

Results for higher topological charge can be found in (see some movies for exact SU(2) solutions with charge 2) :

Pierre van Baal, last updated June 2004. Page first created March 1999.