regarding employment in a consultancy

I was working with a registered consultancy firm from 5th august 2014 till 8th September 2014.Suddenly I discontinued job with them without resignation and notice period because I got new good opportunity.They gave me offer letter through mail and salary slip too for my 1 month total service.I have no appointment letter hard copy with me and they too don’t have any signed document or contract or offer letter with them from my side . They have proof of biometric attendance only. I even don’t need resignation .Now they have send me legal notice to pay 1 month salary. They also informed my current employer about the same,but my current employer told them that they cannt do anything as per law to them and notified me to continue with current employer but current employer will not give any protection in case of any issue to me .I have not shown anywhere to my current employer that I was working with previous consultancy. will my previous(consultancy) take action against me and what are the ways to protect myself?