If you're having issues logging into a match of Zombies, there are a few fixes you can implement to try to get the game running again, but it's not guaranteed that these will resolve it.

For starters, you should check the official Call of Duty updates account to see if the servers are down. If it's a server issue, then there's nothing you can personally do to fix it until the developers push out a patch.

Once you've confirmed that the servers are not down, you can try closing the application and relaunching it. If relaunching regularly doesn't solve the issue, you can also choose to restart it and “Run as Administrator.” To do this, right-click on the title in your library and select "Run as Administrator." This is another method that many have found to work, but this is not a guaranteed solution.

If restarting the game doesn't work, then you may need to verify the game files. On PC, right-click on Modern Warfare 3 in your library and select "Properties." From there, choose "Local Files," and then "Verify integrity of game files."

This will check your files to make sure they aren't corrupted. This is an easier solution than deleting and redownloading the game, though if verifying the files' integrity doesn't work, redownloading the game is the next step.

Finally, if none of the above fixes resolves the issue, you may just have to submit a support ticket and wait for a patch to be put out. Call of Duty games are known to have a litany of issues as of late, so it's possible this is just another bug the developers are dealing with at the moment. Though it's not the ideal solution, it may be time to switch gears and try your hand at a different game on your backlog for the time being.