I have been studying (extended) topological quantum field theories (in short TQFTs) from the mathematical point of view and I have no background of the physics point of view. Sometimes I encountered papers talking about Wilson lines, boundary conditions, surface defects and so on. I looked up these terminology but I couldn't find a good explanation how these are related to TQFTs.

I also want to know the relation of a path integral and a TQFT.

Could you suggest me references (papars, websites, books, vidoes etc) that explains the relationship between these physical jargon and TQFTs from mathematical point of view? Or could you explain here?

Thank you in advance.

(This question was asked in mathstack exchange but there is no answer. Here

  • $\begingroup$ check out Kevin Walker's notes canyon23.net/math $\endgroup$
    – Paul
    Jan 16, 2013 at 3:30

1 Answer 1


Greg Moore recently gave the Felix Klein lectures and a draft of notes for his lectures is available at


You will find in the first few pages a discussion of (extended) TQFT, defects, Wilson lines and so on in a language which I imagine is more suitable to mathematicians than to (most) physicists.


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