Perl: using variable in substitution

Question

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How to use a variable in the replacement side of the Perl substitution operator?

I would like to do something like

$sub = "\\1";
$match = "hi(.*)";
$str = "hi1234"
$res = $str;
$res =~ s/$match/$sub/g

I would like this to return 1234 but in this case it returns \1. I.e. I want it to be equivalent to s/$match/\1/g does anyone know how to do this?