Error with $ when using math in TikZ figure

Question

I am drawing some figures with TikZ for a beamer presentation. I want one figure to look something like this:

Additionally, I want to add labels under the intervals (the sections in between ticks on the axis). When trying to do this, I seem to be making some kind of syntactic mistake (see last section of the code below) - TeX seems to think I am missing a $ or have forgotten }, but I have utterly failed at spotting the mistake after numerous attempts.

I don't feel that well to ask for "debugging" help (since it will likely help no one but me), but considering I am quite pressed for time and still have to do lots of other figures and content... I figure someone might have fun telling me where my code sucks (and the why would be interesting as well). Here is my MWE (which is a beamer document since I will be using overlays for gradually uncovering figures):

\documentclass{beamer}
\usepackage{tikz}
\tikzset{%
  % Styles for visibility and hiding of elements in overlays%
  invisible/.style={opacity=0},%
  visible on/.style={alt=#1{}{invisible}},%
  alt/.code args={<#1>#2#3}{%
    \alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}}% \pgfkeysalso doesn't change the path
}}%
\usetikzlibrary{calc}
\colorlet{excitementcolor}{blue!40!green!70!white}
\colorlet{refractioncolor}{orange!80!white}
\colorlet{restingcolor}{white}

%................................
\begin{document}
  \begin{frame}
    \center
    \begin{tikzpicture}
      \def\shadeheight{2pt}
      \def\tickheight{0.15}
      \tikzset{axisstyle/.style={draw,semithick,fill=black,->}}
      % The shaded background%
      \shade[left color=refractioncolor]%
        (-2.5,-\shadeheight) rectangle (0.2,\shadeheight);%
      \shade[left color=white, right color=excitementcolor]%
        (0.4,-\shadeheight) rectangle (2.5,\shadeheight);%
      % The axis itself%
      \path[axisstyle]%
        (-2.5,0.0) -- (3.1,0) node[right] {$c_{ij}$};
      % Draw big ticks on axis%
      \foreach \x in {-2.5,...,2.5}{
        \draw (\x,-\tickheight) -- (\x,\tickheight); 
      }
      \node[above] at (0,\tickheight) {$0$};

      % Draw interval labels
      \foreach \x/\xt in {-2/$ [-\alpha,-\beta) $, -1/$ [ -\beta, -\gamma) $,  
                           0/$ [-\gamma,\delta) $,  1/$ [\delta,\epsilon)  $,  
                           2/$ [\epsilon,1+r)   $ }{  
        \node[below] at (\x,-\shadeheight) {\xt};
      }

    \end{tikzpicture}
  \end{frame}
\end{document}