I saw in a [lecture](https://www.youtube.com/watch?v=-BleG7PBwEA&list=PLA2FDCCBC7956448F&index=2) (see after [00:55:00](https://youtu.be/-BleG7PBwEA?t=3300)) by Leonard Susskind, he write Polyakov action, saying that the string is supposed to have divided into several pieces with mass (he says that it is the non-relativistic analogue mass) reducing proportionately and disappear eventually as the limit approaches infinity and each is connected with the neighbouring ones with springs.

My question is, if one assumes all strings to have a finite mass, then how does massless particles arise in the theory?