[support] Themed frontpage without $sidebar_right

I'm trying to set different front page for anonymous and authenticated users using the front page module <http://drupal.org/project/front>. I'd like the frontpage to have the header but not the right sidebar. In page.tpl.php the right sidebar is defined as $sidebar_right. So I thought that I could add code to check if the url is domain.com/front_page and then not print $sidebar_right. Or some other solution that doesn't print the right sidebar on the front_page. I'm a php novice but I'm learning.. I appreciate any help I can get. Thanks! /Mattias