$ab = "\$a";

That's taking the value of $a and appending it to a backslash ...

Actually, it's escaping a  $ (dollar) character to make it a literal rather than a scalar sigil, which would result in scalar interpolation:

c:\@Work\Perl\monks>perl -wMstrict -le
"my $a = 'foo';
 my $ab = qq{'\$a'  '$a'};
 print $ab;
"
'$a'  'foo'
[download]

(I have to use  qq{} instead of  "" (double-quotes) to keep Windoze command line from going nuts with escapes.)