Can I watch just one variable changing inside an array of objects in Angular JS?

Is it possible to do a watch on this and watch for just the value of the field a changing

Sure.

If you want to watch only for value a you can define ng-change for (suppose a is a input) input a.

HTML

<div ng-controller="Controller">
   <div ng-repeat="val in abc">
     <input type='text' ng-model='val.a' ng-change="onAChange(val.a)">
     <input type='text' ng-model='val.b'>
  </div>
 </div>

JS

$scope.onAChange = function(mod){
  console.log(mod);
};

Demo 1 Plunker

Other way, to $watch on all object abc and write "deep" watch, something like:

     $scope.$watch(function () {
       return $scope.abc[0].a;
     },
     function (newValue, oldValue) {
     if(newValue == oldValue){return;}

        console.log(newValue, oldValue);

     }, true);

Demo 2 Plunker

As a side note:

You don't need var before $scope.abc.