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\title{My project}
\author{My name}
%\email[]{yannick-meurice@uiowa.edu}
\affiliation{Department of Physics and Astronomy\\ The University of Iowa\\
Iowa City, Iowa 52242, USA }
\date{\today}
\begin{abstract}
Short summary 
\end{abstract}
%\pacs{11.15.-q, 11.15.Ha, 11.15.Me, 12.38.Cy}
\maketitle
\def\gf{\mathfrak{b} }
\def\tc{\lambda^t}
\section{Introduction}
Important references
\cite{bender69}\cite{bender73}\cite{dyson52}

\section{The problem}

\subsection{Basic definitions} 

Just sample equations

In $D$-dimensions, in later sections we set $D=2$

Nonlinear sigma model on a cubic lattice

\begin{equation}
Z=\int \prod _{\bold x} d^N\phi_{\bold x}\delta({\bold \phi}_{\bold x}.{\bold \phi}_{\bold x}-1) {\rm e}^{-(1/g_0^2)E[\{\phi\}]}
\end{equation}
with
\begin{equation}
E[\{\phi\}]=-\sum_{{\bold x},{\bold e}}({\bold \phi}_{\bold x}.{\bold \phi }_{\bold x+e}-1)
\end{equation}

't Hooft coupling:

\begin{equation}
\tc\equiv g_0^2N
\end{equation}
kept constant as $N$ becomes large.

\begin{equation}
b\equiv 1/\tc
\end{equation}

\subsection{Negative coupling duality}

We assume a cubic lattice with an even number of sites in each direction and periodic boundary conditions. Under these conditions

\begin{equation}
Z[-g_0^2]={\rm e}^{2DL^D/g_0^2}Z[g_0^2]
\end{equation}

This can be seen by changing variable $\phi\rightarrow -\phi$ on sublattices with lattice spacing twice larger and such that they share exactly one site with each link of the original lattice.

Similar to $SU(2N)$ pure gauge theories on even lattices. 



\begin{figure}
\hspace{-10pt}
\begin{center}
\includegraphics[width=3.3in,angle=0]{clover.eps}
\end{center}

\caption{
\label{fig:clover} Complex values taken by $\lambda^t$ when $M^2$ varies over the complex plane (here on horizontal and vertical lines in the $M^2$ plane); the circles are inverses of the asymptotic lines in the $1/\lambda^t$ plane.}
\end{figure}

\section{Method used}

\section{Results}

\section{Conclusions}
 
 
\begin{acknowledgments}

We thank so and so for discussions and encouragments. 
This 
research was supported in part  by the Department of Energy
under Contract 

\end{acknowledgments}

\begin{thebibliography}{3}
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\bibitem[{\citenamefont{Bender and Wu}(1969)}]{bender69}
\bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Bender}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{T.~T.} \bibnamefont{Wu}},
  \bibinfo{journal}{Phys. Rev.} \textbf{\bibinfo{volume}{184}},
  \bibinfo{pages}{1231} (\bibinfo{year}{1969}).

\bibitem[{\citenamefont{Bender and Wu}(1973)}]{bender73}
\bibinfo{author}{\bibfnamefont{C.~M.} \bibnamefont{Bender}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{T.~T.} \bibnamefont{Wu}},
  \bibinfo{journal}{Phys. Rev.} \textbf{\bibinfo{volume}{D7}},
  \bibinfo{pages}{162O} (\bibinfo{year}{1973}).

\bibitem[{\citenamefont{Dyson}(1952)}]{dyson52}
\bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{Dyson}},
  \bibinfo{journal}{Phys. Rev.} \textbf{\bibinfo{volume}{85}},
  \bibinfo{pages}{631} (\bibinfo{year}{1952}).

\end{thebibliography}

\end{document}