... in which case you don't need the substition at all :)

$_ = "master442arb_ba";
$_ =~ /master(.*)arb_ba/;
$_ = "m$1a_ba";
print $_;    # m442a_ba
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(the s/$_/$action/ in your snippet looks for "master442arb_ba" in "master442arb_ba" and replaces this (i.e. itself) with "m442a_ba" — an assignment is shorter...)