mathematics - What areas of physics depend on the sum $1 + 2 + 3 + 4 + 5 + 6+ 7+ldots= -1/12$?

This youtube video from Numberphile, http://youtu.be/w-I6XTVZXww

shows how the value is derived. In the video, one interviewee claims that "this result is used in many areas of physics". In the video, only string theory is mentioned.

Which areas of physics use or depend on the sum $$1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12?$$