permission denied upon mkdir

I use mkdir() to create a directory on my server:

// $var_name is equal to an md5() hash
$path = "/var/www/publish/" . $var_name;
if(mkdir($path)) {
  echo "success";
} else {
  echo "error";
}

This will yield an error due to a permission denied. Looking up on my server, by doing ls -lh

drwxr-xr-x  2 root     root   4.0K Aug 17 09:05   publish

But if my $path is equal to $path = "/var/www/" . $var_name; it will create the folder I expected. What seems to be the issue in here.