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\begin{document}

\vskip -4cm


\begin{flushright}
FTUAM-98-17

IFT-UAM/CSIC-98-12
\end{flushright}

\vskip 0.2cm

{\Large
\centerline{{\bf Self-dual vortex-like  configurations}}
\centerline{{\bf in SU(2) Yang-Mills Theory}}
\vskip 0.3cm

\centerline{\qquad \ \ 
  A. Gonz\'alez-Arroyo{$^\dag$}{$^\ddag$} and A. Montero{$^\dag$} \\ }}
\vskip 0.3cm

\centerline{{$^\dag$}Departamento de F\'{\i}sica Te\'orica C-XI,}
\centerline{Universidad Aut\'onoma de Madrid,}
\centerline{Cantoblanco, Madrid 28049, SPAIN.}
\vskip 10pt
\centerline{{$^\ddag$}Instituto de F\'{\i}sica Te\'orica C-XVI,}
\centerline{Universidad Aut\'onoma de Madrid,}
\centerline{Cantoblanco, Madrid 28049, SPAIN.}

\vskip 0.8cm

\begin{center}
{\bf ABSTRACT}
\end{center}
We show that there are  solutions of the SU(2) Yang-Mills classical
equations of motion in $R^4$,  which are self-dual and vortex-like(fluxons).
The action density is concentrated along a thick two-dimensional wall
(the world sheet of a straight infinite vortex line). The configurations
are constructed   from self-dual $R^2 \times T^2$ configurations.


\vskip 1.5 cm
\begin{flushleft}
PACS: 11.15.-q, 11.15.Ha

Keywords: Vortices, Fluxons, Instanton solutions, Lattice gauge theory, 
Confinement.
\end{flushleft}

\newpage

\input{section1.tex} 


\input{section2.tex}


\input{section3.tex}




\input{acknow.tex}


\newpage



\begin{thebibliography}{10}


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\newblock {\em   J. Phys. A. } 26 (1993) 2667.


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\newblock {\em Nucl. Phys.  } B413 (1994) 535;
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\newblock {\em Nucl. Phys.} B429 (1994) 451.


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\newblock {\em Phys. Lett.} 104B (1981) 61;
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\newblock {Proceedings of the 1997 Pe\~n\'{\i}scola Advanced School in
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hep-th/9807108.


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\end{thebibliography}
\newpage

\begin{figure}

\caption{We plot the logarithm of the the energy profile $\Epsilon_{0}$(t) for our
solution. Open circles and full squares correspond to lattice spacing
values of  $a=0.1666$ and $0.25$ respectively. The straight line is given by
$5.42 - 6.5 \, t$.}

\vbox{ \hskip -1cm \hbox{  \epsfxsize=450pt \hbox{\epsffile{logper.eps} }
}  
     }
     
     \label{profile }
     
     \end{figure}
     
     
     \newpage
     
     \begin{figure}

     \caption{ We plot the value of the trace of an $r \times r$  Wilson loop
     centered around the vortex ${\cal L}(r,x,z)$. The different points are
 labeled in the figure, with  {\em max} corresponding to $x=z=0$ and  {\em
min} to  $x=z=\frac{1}{2}$.}
     
     \vbox{ \hskip -1cm \hbox{  \epsfxsize=450pt
\hbox{\epsffile{wilson.eps} }
}  
     }
     
          \label{wilsonloop}
	  
	       \end{figure}
	       
	       
	            \newpage
		    
     
\end{document}


