MongoDB : aggregation framework : $match between fields

I have a test collection with two documents :

> db.test.find().pretty()
{ "_id" : ObjectId("510114b46c1a3a0f6e5dd7aa"), "a" : 1, "b" : 2 }
{ "_id" : ObjectId("510114c86c1a3a0f6e5dd7ab"), "a" : 3, "b" : 1 }

With aggregation framework, I want to get only the documents where a is greater than b. $gt get only values in argument not fields...

> db.test.aggregate([{"$match":{"$a":{"$gt":"$b"}}}])
{ "result" : [ ], "ok" : 1 } /* don't work*/

Do you have some ideas ?

Thanks in advance

Best regards