I was browsing through Foundations of Space and Time, a compilation of essays on various theories of quantum gravity. The following passage in the introduction intrigued me:


  Each compactification leads to a different vacuum state.... at least one state should describe our Universe in its entirety.... the enormous number (~10^500 at last count) of solutions, with no perturbative mechanism to select mechanism to select among them, leads some critics to question the predictive power of the theory..Even more worrying is that, while the theory is perturbatively finite order by order, the perturbation series does not seem to converge.


I don't know anything about string theory and so I could not make head or tails this. All I know is that ~$10^{500}$    is a very large number. 


What exactly is a 'solution' in string theory? Is it a spacetime metric of some sort or the terms of a S-matrix of some sort?  
Why are there so many 'solutions'? 
I thought string theory was supposed to be finite, why do perturbative series still diverge?
Is there any experimental technique to limit the number of 'solutions'?  
Will experimental techniques be able to pinpoint a solution within present day string theorists' lifetimes too? If not, how long will it take before we can experimentally probe these things? 
Are string theorists completely relaxed about these issues? Or are they in anguish? 



Question: How can I superimpose LaTeX / TeX output over a PDF file?
Answer: You can use TikZ to place the form as image at the center of an otherwise empty page and then draw on it. This is similar to the suggested pdfpages solution but avoid passing around the tikzpictures, which isn't really necessary. 

See also Drawing on an image with TikZ and Is there the easiest way to toggle (show/hide) navigational grids in TikZ? for related code.

You could even add real PDF form fields to it. See Creating fillable PDFs for how it can be done.

\documentclass[letterpaper]{article}% ensure identical page size

\usepackage{tikz}

\pagestyle{empty}
\begin{document}
% Page 1
\begin{tikzpicture}[remember picture,overlay]
    \node at (current page.center) {\includegraphics[page=1]{form}};
    \begin{scope}[shift={(current page.south west)},every node/.style={anchor=base west}]
        % Grid to help find the positions (remove in final version)
        \draw [help lines] (0,0) grid (current page.north east);
        \draw [help lines,thick] (0,0) grid [step=5cm] (current page.north east);
        %
        \node at (2cm,9.75cm) {John Doe};
        \node at (13cm,9.75cm) {\today};
    \end{scope}
\end{tikzpicture}
\clearpage
% Page 2
\begin{tikzpicture}[remember picture,overlay]
    \node at (current page.center) {\includegraphics[page=2]{form}};
    \begin{scope}[shift={(current page.south west)},every node/.style={anchor=base west}]
        % Grid to help find the positions (remove in final version)
        \draw [help lines] (0,0) grid (current page.north east);
        \draw [help lines,thick] (0,0) grid [step=5cm] (current page.north east);
        %
        %\node at (2.5cm,10.75cm) {John Doe};
    \end{scope}
\end{tikzpicture}
\clearpage
\end{document}


This example used the IEEE copyright form. Just download it and rename it to form.pdf. The second page actually does not include any fillable form fields, but I found it important to show how to handle multiple pages.