Sent resignation mail and have not served notice period.

Dear All, I was working in an IT company. Employee strength of that company is around 10. I was employed at the company for 2 and half months and then i got an opportunity for higher education. So i took the opportunity. Next day i went to office and I informed HR that I have opportunity for higher education and i would like to pursue it. After having talked with hr, I mailed my resignation letter to them. HR got agitated and i tried to explain him about the opportunity as it was something i could not miss. After that HR and director of the company threatened me that they will take legal actions against me. I, on my part told them about this in person as I didn’t want to abscond. What are the legal actions that they can take against me ? And what can i do to end this in a peaceful way ? In my letter of employment, it is written that The employee may terminate this agreement by giving not less than 3 months written notice to the employer. In case the employee terminates services without the 3 months notice period, the employee will be liable to pay the damages and loss of business due to the breach of the notice period clause. The employer may terminate this agreement by giving not less than 15 days of written notice when the employee is on probation or not less than 1 month of notice period, when the employee is confirmed.