regex - Nginx server_name regexpが変数として機能しない

Question

このようなエラーがまだ発生する理由を教えてくれる人はいますか?

Restarting nginx: [emerg]: unknown "domain_name" variable
configuration file /etc/nginx/nginx.conf test failed

変数であるコードの部分は次のようになります。

server {
    # if you're running multiple servers, instead of "default" you should
    # put your main domain name here
    listen 80 default;

    # you could put a list of other domain names this application answers
    server_name ^~(?<domain_name>[^\.]*)\.(?<tld>[^\.]*)$;

    # root defined by domain
    root /home/deployer/apps/$domain_name/current/;

    # access && error && rewrite log
    access_log /var/log/nginx/access.log;
    error_log /var/log/nginx/error.log;
    rewrite_log on;

    # default location
    location / {

...