Hi, Venkatesh here.
Two years back I got an accident and broke my upper front two teeth. On visiting the dentist , he advised me to go for the crowns without suggesting for root canal. And I went as he said. And now after two years due to severe pain of teeth I again went to different dentist and on examining he said that the abscess has been formed on the gums of the upper front teeth. As per him the only way to treat the abscess is root canal. As the tooth is already having the crown the dentist said that he will try to do the root canal directly on the crown and with extra care he said that he will try to save the present crown. So I agreed with him and went with the treatment of root canal 2 days back. Dentist left the hole open without filling intentionally so that the abscess will drain off. And within a day I guess the abscess had beed drained off as I feel much much better and it has beed dissapered. So my serious question is now is it compulsory for me to go for the new crown or is it OK if I just make that hole filled permanently.

This dentist sounds like he knows what he's doing. Go with his advice. Sometimes the crown can be saved and sometimes it can't. If he says it can't, ask why, and use your judgment.

If the crown did not break, there is NO reason you need a new crown placed. Your DDS can place a filling material over the opening that was made in the crown where the DDS did the RC through.
Good Luck!