How can I get an absolute path to a theme?
The base_path() function would return the base bath of the Drupal installation


  Returns the base URL path of the Drupal installation. At the very
  least, this will always default to /.


and path_to_theme() will return the path to the current theme.


  Return the path to the current themed element.
  
  It can point to the active theme or the module handling a themed
  implementation. For example, when invoked within the scope of a
  theming call it will depend on where the theming function is handled.
  If implemented from a module, it will point to the module. If
  implemented from the active theme, it will point to the active theme.
  When called outside the scope of a theming call, it will always point
  to the active theme.