Reading variable from a txt file using bash

I'm new to bash. I'm trying to write a script that will read data from a text find and declare some variables. In the example below we read from a tab delimited file "ab.txt" that looks like this: a->AA b->BB Where -> denotes a tab. I'm reading this data with this code:

#!/bin/bash
while read line
do
	tmp=(${line///})
	fieldName=${tmp}
	
	case $fieldName in
	"a")
		a=${tmp}
		;;
	"b")
		b=${tmp}
		;;
	esac
		
done < "ab.txt"


echo "a:"
echo $a	

echo "b:"
echo $b

echo "concat a,b"
echo $a$b

echo "concat b,a"
echo $b$a

This gives me "a" and "b" nicely, but will not concatenate a and b! The output is this:

a:
AA
b:
BB
concat a,b
BB
concat b,a
AA

What am I doing wrong?